diff --git "a/data/records.jsonl" "b/data/records.jsonl" --- "a/data/records.jsonl" +++ "b/data/records.jsonl" @@ -38,6 +38,10 @@ {"case": "cirinhex@18", "density": 0.81913146509039, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@18", "credit": "Trivial", "date": "", "family_updated": "7/19/12", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "223b1a3f7b7d0e67", "improvement": -0.000759899456760138, "max_boundary_excess": -1.33856736717064e-06, "max_pair_overlap_depth": -1.657857602177515e-05, "metric_expression": "5.15476", "metric_symbol": "s", "metric_value": 5.15475989945676, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.154, "setup": "cirinhex", "side": 5.15475989945676, "solution_path": "data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/223b1a3f7b7d0e67.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinhex@19", "density": 0.8646358262071194, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@19", "credit": "Trivial", "date": "", "family_updated": "7/19/12", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "78f9327e80d8ab20", "improvement": -0.0007686707015803762, "max_boundary_excess": -6.035946609195264e-07, "max_pair_overlap_depth": -1.6136694912294303e-05, "metric_expression": "5.15477", "metric_symbol": "s", "metric_value": 5.15476867070158, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.154, "setup": "cirinhex", "side": 5.15476867070158, "solution_path": "data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/78f9327e80d8ab20.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinhex@20", "density": 0.7503080962551325, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "5.676+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.676, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@20", "credit": "David W", "date": "July 2012", "family_updated": "7/19/12", "metric_expression": "5.676+", "metric_symbol": "s", "metric_value": 5.676, "reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "247c6c06779a7d8b", "improvement": -0.0013304688728235092, "max_boundary_excess": -7.66649728101143e-06, "max_pair_overlap_depth": -2.983410910761819e-05, "metric_expression": "5.67733", "metric_symbol": "s", "metric_value": 5.677330468872824, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.676, "setup": "cirinhex", "side": 5.677330468872824, "solution_path": "data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/247c6c06779a7d8b.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinhex@21", "density": 0.7789652581067265, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "friedman_metric_expression": "5.709+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.709, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@21", "credit": "David W", "date": "July 2012", "family_updated": "7/19/12", "metric_expression": "5.709+", "metric_symbol": "s", "metric_value": 5.709, "reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "38040eceeb63c1e3", "improvement": -0.0005199689632231497, "max_boundary_excess": -9.315374129847953e-06, "max_pair_overlap_depth": -3.751451804223649e-05, "metric_expression": "5.70952", "metric_symbol": "s", "metric_value": 5.709519968963223, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.709, "setup": "cirinhex", "side": 5.709519968963223, "solution_path": "data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/38040eceeb63c1e3.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinhex@22", "density": 0.7509530082141859, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "friedman_metric_expression": "5.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.952, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@22", "credit": "David W", "date": "July 2012", "family_updated": "7/19/12", "metric_expression": "5.952+", "metric_symbol": "s", "metric_value": 5.952, "reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cd7262f9f7d0d279", "improvement": 0.0001229278734493633, "max_boundary_excess": -6.663138574891647e-06, "max_pair_overlap_depth": -3.268885699680979e-05, "metric_expression": "5.95188", "metric_symbol": "s", "metric_value": 5.951877072126551, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.952, "setup": "cirinhex", "side": 5.951877072126551, "solution_path": "data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cd7262f9f7d0d279.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinhex@23", "density": 0.7694641578789073, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "friedman_metric_expression": "34/7 + 2/\u221a3 = 6.011+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.011, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@23", "credit": "David W", "date": "July 2012", "family_updated": "7/19/12", "metric_expression": "34/7 + 2/\u221a3 = 6.011+", "metric_symbol": "s", "metric_value": 6.011, "reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "de2d2aabdc650ad2", "improvement": -0.0009964252593954726, "max_boundary_excess": -6.1931154748950945e-06, "max_pair_overlap_depth": -3.920500316656472e-05, "metric_expression": "6.01200", "metric_symbol": "s", "metric_value": 6.011996425259396, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.011, "setup": "cirinhex", "side": 6.011996425259396, "solution_path": "data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/de2d2aabdc650ad2.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinhex@24", "density": 0.7747882438352293, "friedman_analytical_or_proved": false, "friedman_credit": "Rob Pratt", "friedman_date": "March 2020", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "friedman_metric_expression": "6.117+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.117, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@24", "credit": "Rob Pratt", "date": "March 2020", "family_updated": "7/19/12", "metric_expression": "6.117+", "metric_symbol": "s", "metric_value": 6.117, "reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "source_image": "hc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "friedman_source_image": "hc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "61a86ae12328c1ca", "improvement": -0.003164603994216364, "max_boundary_excess": -3.4542492504119338e-06, "max_pair_overlap_depth": -2.04098607499148e-05, "metric_expression": "6.12016", "metric_symbol": "s", "metric_value": 6.120164603994216, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.117, "setup": "cirinhex", "side": 6.120164603994216, "solution_path": "data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/61a86ae12328c1ca.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinpen@1", "density": 0.8647965566225578, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "1.453+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.453, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@1", "credit": "Trivial", "date": "", "family_updated": "7/10/12", "metric_expression": "1.453+", "metric_symbol": "s", "metric_value": 1.453, "reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "source_image": "pent.1.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "friedman_source_image": "pent.1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "2249439da521383e", "improvement": -9.321311914245456e-05, "max_boundary_excess": -4.798939718275719e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.45309", "metric_symbol": "s", "metric_value": 1.4530932131191425, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.453, "setup": "cirinpen", "side": 1.4530932131191425, "solution_path": "data/solutions/generated/cirinpen_001_2249439da521383e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2249439da521383e.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinpen@2", "density": 0.5049856179230741, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "2.689+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.689, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@2", "credit": "Trivial", "date": "", "family_updated": "7/10/12", "metric_expression": "2.689+", "metric_symbol": "s", "metric_value": 2.689, "reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "source_image": "pent.2.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "friedman_source_image": "pent.2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "042df6c460b769f5", "improvement": -0.00021758992828191381, "max_boundary_excess": -8.904067621218203e-06, "max_pair_overlap_depth": -5.9422400474407056e-05, "metric_expression": "2.68922", "metric_symbol": "s", "metric_value": 2.689217589928282, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.689, "setup": "cirinpen", "side": 2.689217589928282, "solution_path": "data/solutions/generated/cirinpen_002_042df6c460b769f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/042df6c460b769f5.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinpen@3", "density": 0.6022625992350803, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.015+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.015, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@3", "credit": "George Sicherman", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "3.015+", "metric_symbol": "s", "metric_value": 3.015, "reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "source_image": "pent.3.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "7afe63c4f78d1c3c", "improvement": -0.0009082861357154748, "max_boundary_excess": -2.348511423333477e-06, "max_pair_overlap_depth": -3.760319804513301e-05, "metric_expression": "3.01591", "metric_symbol": "s", "metric_value": 3.0159082861357156, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.015, "setup": "cirinpen", "side": 3.0159082861357156, "solution_path": "data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7afe63c4f78d1c3c.svg", "tolerance": 1e-08, "verified": true} @@ -58,6 +62,10 @@ {"case": "cirinpen@18", "density": 0.7574722105185439, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.586+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.586, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@18", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "6.586+", "metric_symbol": "s", "metric_value": 6.586, "reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "34fda06736bbaaf7", "improvement": -0.0012379322999080955, "max_boundary_excess": -8.803338162222119e-06, "max_pair_overlap_depth": -4.5158559001112764e-05, "metric_expression": "6.58724", "metric_symbol": "s", "metric_value": 6.587237932299908, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.586, "setup": "cirinpen", "side": 6.587237932299908, "solution_path": "data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/34fda06736bbaaf7.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinpen@19", "density": 0.7551620068495595, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.777+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.777, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@19", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "6.777+", "metric_symbol": "s", "metric_value": 6.777, "reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "dfaba7cef14e53f5", "improvement": -0.0010877146457399789, "max_boundary_excess": -3.911905938958071e-06, "max_pair_overlap_depth": -5.528697090007029e-05, "metric_expression": "6.77809", "metric_symbol": "s", "metric_value": 6.77808771464574, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.777, "setup": "cirinpen", "side": 6.77808771464574, "solution_path": "data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dfaba7cef14e53f5.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinpen@20", "density": 0.7572204985441312, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.944+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.944, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@20", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "6.944+", "metric_symbol": "s", "metric_value": 6.944, "reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "d513055d785b23f7", "improvement": -0.0007124298362715109, "max_boundary_excess": -3.4085836122521584e-06, "max_pair_overlap_depth": -2.3984136221066876e-05, "metric_expression": "6.94471", "metric_symbol": "s", "metric_value": 6.9447124298362715, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.944, "setup": "cirinpen", "side": 6.9447124298362715, "solution_path": "data/solutions/generated/cirinpen_020_d513055d785b23f7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d513055d785b23f7.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinpen@21", "density": 0.7549642211430954, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "friedman_metric_expression": "7.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.107, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@21", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "7.107+", "metric_symbol": "s", "metric_value": 7.107, "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "6869ffb03b036ff3", "improvement": -0.01983841780610529, "max_boundary_excess": -5.581345224214829e-06, "max_pair_overlap_depth": -4.1181747931773316e-05, "metric_expression": "7.12684", "metric_symbol": "s", "metric_value": 7.1268384178061055, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.107, "setup": "cirinpen", "side": 7.1268384178061055, "solution_path": "data/solutions/generated/cirinpen_021_6869ffb03b036ff3.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6869ffb03b036ff3.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinpen@22", "density": 0.7595290345154431, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "friedman_metric_expression": "7.271+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.271, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@22", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "7.271+", "metric_symbol": "s", "metric_value": 7.271, "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "ebdb05232e56526e", "improvement": -0.0015983061562394596, "max_boundary_excess": -9.413438632810411e-06, "max_pair_overlap_depth": -6.856237147889743e-05, "metric_expression": "7.27260", "metric_symbol": "s", "metric_value": 7.272598306156239, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.271, "setup": "cirinpen", "side": 7.272598306156239, "solution_path": "data/solutions/generated/cirinpen_022_ebdb05232e56526e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ebdb05232e56526e.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinpen@23", "density": 0.7675010590620791, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "friedman_metric_expression": "7.397+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.397, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@23", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "7.397+", "metric_symbol": "s", "metric_value": 7.397, "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "0115bd21477c01e6", "improvement": -0.0003280102549396702, "max_boundary_excess": -7.583943801847681e-07, "max_pair_overlap_depth": -3.4243400256706025e-05, "metric_expression": "7.39733", "metric_symbol": "s", "metric_value": 7.39732801025494, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.397, "setup": "cirinpen", "side": 7.39732801025494, "solution_path": "data/solutions/generated/cirinpen_023_0115bd21477c01e6.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0115bd21477c01e6.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinpen@24", "density": 0.7719374015643087, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "friedman_metric_expression": "7.534+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.534, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@24", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "7.534+", "metric_symbol": "s", "metric_value": 7.534, "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "9eb26a95274f1d1d", "improvement": -0.0006837609794780874, "max_boundary_excess": -2.468927518428643e-06, "max_pair_overlap_depth": -2.3713548386705696e-05, "metric_expression": "7.53468", "metric_symbol": "s", "metric_value": 7.534683760979478, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.534, "setup": "cirinpen", "side": 7.534683760979478, "solution_path": "data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9eb26a95274f1d1d.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinsqu@1", "density": 0.7853971453379307, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@1", "credit": "Trivial", "date": "", "family_updated": "10/9/10", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "cs1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "cs1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "329c377d412c468f", "improvement": -1.2962348967526793e-06, "max_boundary_excess": -1.0795596527835016e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "2.00000", "metric_symbol": "s", "metric_value": 2.0000012962348968, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "cirinsqu", "side": 2.0000012962348968, "solution_path": "data/solutions/generated/cirinsqu_001_329c377d412c468f.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/329c377d412c468f.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinsqu@2", "density": 0.5390070210000131, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + \u221a2 = 3.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.414, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@2", "credit": "Trivial", "date": "", "family_updated": "10/9/10", "metric_expression": "2 + \u221a2 = 3.414+", "metric_symbol": "s", "metric_value": 3.414, "reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "source_image": "cs2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "friedman_source_image": "cs2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e3bab8445b304ebe", "improvement": -0.00022959896202801033, "max_boundary_excess": -2.1788679802625666e-06, "max_pair_overlap_depth": -1.6252235923275293e-05, "metric_expression": "3.41423", "metric_symbol": "s", "metric_value": 3.414229598962028, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.414, "setup": "cirinsqu", "side": 3.414229598962028, "solution_path": "data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e3bab8445b304ebe.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinsqu@3", "density": 0.6096071430698954, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.931, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@3", "credit": "Trivial", "date": "", "family_updated": "10/9/10", "metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "metric_symbol": "s", "metric_value": 3.931, "reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "source_image": "cs3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "friedman_source_image": "cs3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "63c314af1da3741c", "improvement": -0.0009731189575252763, "max_boundary_excess": -9.540614135605807e-06, "max_pair_overlap_depth": -7.777950709542125e-05, "metric_expression": "3.93197", "metric_symbol": "s", "metric_value": 3.9319731189575253, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.931, "setup": "cirinsqu", "side": 3.9319731189575253, "solution_path": "data/solutions/generated/cirinsqu_003_63c314af1da3741c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/63c314af1da3741c.svg", "tolerance": 1e-08, "verified": true} @@ -78,6 +86,10 @@ {"case": "cirinsqu@18", "density": 0.7546080214690231, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 24/\u221a13 = 8.656+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.656, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@18", "credit": "Peikert", "date": "1991", "family_updated": "10/9/10", "metric_expression": "2 + 24/\u221a13 = 8.656+", "metric_symbol": "s", "metric_value": 8.656, "reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "source_image": "cs18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "friedman_source_image": "cs18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "4872462eca76de82", "improvement": -0.0006623865813519814, "max_boundary_excess": -5.585640835636951e-06, "max_pair_overlap_depth": -5.7251545610981225e-05, "metric_expression": "8.65666", "metric_symbol": "s", "metric_value": 8.656662386581353, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.656, "setup": "cirinsqu", "side": 8.656662386581353, "solution_path": "data/solutions/generated/cirinsqu_018_4872462eca76de82.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4872462eca76de82.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinsqu@19", "density": 0.752224113091453, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8.907+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.907, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@19", "credit": "Peikert", "date": "1991", "family_updated": "10/9/10", "metric_expression": "8.907+", "metric_symbol": "s", "metric_value": 8.907, "reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "source_image": "cs19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "friedman_source_image": "cs19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "72fa8cf8e074fd32", "improvement": -0.0009569875134012307, "max_boundary_excess": -9.019564082723974e-06, "max_pair_overlap_depth": -6.564483433546542e-05, "metric_expression": "8.90796", "metric_symbol": "s", "metric_value": 8.907956987513401, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.907, "setup": "cirinsqu", "side": 8.907956987513401, "solution_path": "data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/72fa8cf8e074fd32.svg", "tolerance": 1e-08, "verified": true} {"case": "cirinsqu@20", "density": 0.7794478091956536, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.978, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@20", "credit": "Peikert", "date": "1991", "family_updated": "10/9/10", "metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "metric_symbol": "s", "metric_value": 8.978, "reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "source_image": "cs20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "friedman_source_image": "cs20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "ed16784370181dab", "improvement": -0.0003475703211961445, "max_boundary_excess": -1.3975782322539487e-06, "max_pair_overlap_depth": -5.140241392753708e-05, "metric_expression": "8.97835", "metric_symbol": "s", "metric_value": 8.978347570321196, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.978, "setup": "cirinsqu", "side": 8.978347570321196, "solution_path": "data/solutions/generated/cirinsqu_020_ed16784370181dab.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ed16784370181dab.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinsqu@21", "density": 0.7531827030031223, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "friedman_metric_expression": "9.358+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.358, "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@21", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "10/9/10", "metric_expression": "9.358+", "metric_symbol": "s", "metric_value": 9.358, "reference_text": "s = 9.358+", "source_image": "cs21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 9.358+", "friedman_source_image": "cs21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "65afc927a4d3cb10", "improvement": -0.0011070505635846217, "max_boundary_excess": -6.857662265602471e-06, "max_pair_overlap_depth": -3.291297220409106e-05, "metric_expression": "9.35911", "metric_symbol": "s", "metric_value": 9.359107050563585, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.358, "setup": "cirinsqu", "side": 9.359107050563585, "solution_path": "data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/65afc927a4d3cb10.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinsqu@22", "density": 0.7716499915329439, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "friedman_metric_expression": "9.463+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.463, "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@22", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "10/9/10", "metric_expression": "9.463+", "metric_symbol": "s", "metric_value": 9.463, "reference_text": "s = 9.463+", "source_image": "cs22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 9.463+", "friedman_source_image": "cs22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "27d48d864449f174", "improvement": -0.0010297949122062278, "max_boundary_excess": -1.1647620365984324e-06, "max_pair_overlap_depth": -2.796224374757017e-05, "metric_expression": "9.46403", "metric_symbol": "s", "metric_value": 9.464029794912205, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.463, "setup": "cirinsqu", "side": 9.464029794912205, "solution_path": "data/solutions/generated/cirinsqu_022_27d48d864449f174.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/27d48d864449f174.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinsqu@23", "density": 0.7628623175184639, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "friedman_metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.727, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@23", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "10/9/10", "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "metric_symbol": "s", "metric_value": 9.727, "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "source_image": "cs23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_source_image": "cs23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "cfa99060ee2203a1", "improvement": -0.005306391434194424, "max_boundary_excess": -1.8298221013957061e-06, "max_pair_overlap_depth": -2.6081243190478887e-05, "metric_expression": "9.73231", "metric_symbol": "s", "metric_value": 9.732306391434195, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.727, "setup": "cirinsqu", "side": 9.732306391434195, "solution_path": "data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cfa99060ee2203a1.svg", "tolerance": 1e-08, "verified": true} +{"case": "cirinsqu@24", "density": 0.7749295071503051, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "friedman_metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@24", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "10/9/10", "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "metric_symbol": "s", "metric_value": 9.863, "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "source_image": "cs24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "friedman_source_image": "cs24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e2eca298edbdb88c", "improvement": -0.0009181131343805049, "max_boundary_excess": -8.506144878683841e-06, "max_pair_overlap_depth": -4.0021533562306644e-05, "metric_expression": "9.86392", "metric_symbol": "s", "metric_value": 9.86391811313438, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.863, "setup": "cirinsqu", "side": 9.86391811313438, "solution_path": "data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e2eca298edbdb88c.svg", "tolerance": 1e-08, "verified": true} {"case": "cirintri@1", "density": 0.6045962978262086, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2\u221a3 = 3.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@1", "credit": "Trivial", "date": "", "family_updated": "7/19/02", "metric_expression": "2\u221a3 = 3.464+", "metric_symbol": "s", "metric_value": 3.464, "reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "source_image": "ct1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "friedman_source_image": "ct1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "10a7a380c7f5376a", "improvement": -0.00011161401610815247, "max_boundary_excess": -1.7091087705090047e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.46411", "metric_symbol": "s", "metric_value": 3.464111614016108, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.464, "setup": "cirintri", "side": 3.464111614016108, "solution_path": "data/solutions/generated/cirintri_001_10a7a380c7f5376a.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/10a7a380c7f5376a.svg", "tolerance": 1e-08, "verified": true} {"case": "cirintri@2", "density": 0.48598475821399, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@2", "credit": "Trivial", "date": "", "family_updated": "7/19/02", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "f5cde1b8295da3ad", "improvement": -0.00022144929157175142, "max_boundary_excess": -3.7587277048611867e-06, "max_pair_overlap_depth": -7.068795172848752e-05, "metric_expression": "5.46422", "metric_symbol": "s", "metric_value": 5.464221449291572, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.464, "setup": "cirintri", "side": 5.464221449291572, "solution_path": "data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f5cde1b8295da3ad.svg", "tolerance": 1e-08, "verified": true} {"case": "cirintri@3", "density": 0.7289907317557431, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@3", "credit": "Trivial", "date": "", "family_updated": "7/19/02", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "fcee9d6e8b7c5ce0", "improvement": -0.000170499845251193, "max_boundary_excess": -1.0755666179917966e-07, "max_pair_overlap_depth": -5.0474041760395494e-05, "metric_expression": "5.46417", "metric_symbol": "s", "metric_value": 5.464170499845252, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.464, "setup": "cirintri", "side": 5.464170499845252, "solution_path": "data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/fcee9d6e8b7c5ce0.svg", "tolerance": 1e-08, "verified": true} @@ -138,6 +150,10 @@ {"case": "domintri@18", "density": 0.8433917909368376, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+4\u221a3 = 9.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.9282, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "3+4\u221a3 = 9.92820+", "metric_symbol": "s", "metric_value": 9.9282, "reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "286272298adf99a4", "improvement": -0.00035960973454685075, "max_boundary_excess": -4.814371048432239e-06, "max_pair_overlap_depth": -1.8972863250255045e-05, "metric_expression": "9.92856", "metric_symbol": "s", "metric_value": 9.928559609734547, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.9282, "setup": "domintri", "side": 9.928559609734547, "solution_path": "data/solutions/generated/domintri_018_286272298adf99a4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/286272298adf99a4.svg", "tolerance": 1e-08, "verified": true} {"case": "domintri@19", "density": 0.7735444652506167, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "8+4/\u221a3 = 10.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "8+4/\u221a3 = 10.30940+", "metric_symbol": "s", "metric_value": 10.3094, "reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "549d560736459f75", "improvement": -0.34180733668304164, "max_boundary_excess": -1.8670172809952138e-05, "max_pair_overlap_depth": -1.0311598933832045e-05, "metric_expression": "10.65121", "metric_symbol": "s", "metric_value": 10.651207336683042, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.3094, "setup": "domintri", "side": 10.651207336683042, "solution_path": "data/solutions/generated/domintri_019_549d560736459f75.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/549d560736459f75.svg", "tolerance": 1e-08, "verified": true} {"case": "domintri@20", "density": 0.7733493858543649, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+2\u221a3 = 10.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.4641, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "7+2\u221a3 = 10.46410+", "metric_symbol": "s", "metric_value": 10.4641, "reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "1be96e85f810fe3e", "improvement": -0.4651863607413542, "max_boundary_excess": -3.72350908996398e-06, "max_pair_overlap_depth": -7.249978854950712e-05, "metric_expression": "10.92929", "metric_symbol": "s", "metric_value": 10.929286360741354, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.4641, "setup": "domintri", "side": 10.929286360741354, "solution_path": "data/solutions/generated/domintri_020_1be96e85f810fe3e.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1be96e85f810fe3e.svg", "tolerance": 1e-08, "verified": true} +{"case": "domintri@21", "density": 0.7704954542050007, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "friedman_metric_expression": "2+5\u221a3 = 10.66025+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.66025, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@21", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "2+5\u221a3 = 10.66025+", "metric_symbol": "s", "metric_value": 10.66025, "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "de2eca0c1c28a96d", "improvement": -0.5596577659107993, "max_boundary_excess": -3.3920242839708145e-06, "max_pair_overlap_depth": -3.2351846175115995e-05, "metric_expression": "11.21991", "metric_symbol": "s", "metric_value": 11.219907765910799, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.66025, "setup": "domintri", "side": 11.219907765910799, "solution_path": "data/solutions/generated/domintri_021_de2eca0c1c28a96d.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/de2eca0c1c28a96d.svg", "tolerance": 1e-08, "verified": true} +{"case": "domintri@22", "density": 0.8205684661731125, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "friedman_metric_expression": "4(1+\u221a3) = 10.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.9282, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@22", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "4(1+\u221a3) = 10.92820+", "metric_symbol": "s", "metric_value": 10.9282, "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6301aae692a9ac9b", "improvement": -0.19983821886336273, "max_boundary_excess": -7.931828549005361e-06, "max_pair_overlap_depth": -1.949750011775997e-05, "metric_expression": "11.12804", "metric_symbol": "s", "metric_value": 11.128038218863363, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.9282, "setup": "domintri", "side": 11.128038218863363, "solution_path": "data/solutions/generated/domintri_022_6301aae692a9ac9b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6301aae692a9ac9b.svg", "tolerance": 1e-08, "verified": true} +{"case": "domintri@23", "density": 0.8238455629873455, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "friedman_metric_expression": "10+2/\u221a3 = 11.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.1547, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@23", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "10+2/\u221a3 = 11.15470+", "metric_symbol": "s", "metric_value": 11.1547, "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "7b6e8b12db0049b9", "improvement": -0.20078516612478836, "max_boundary_excess": -3.686846371587619e-06, "max_pair_overlap_depth": -4.6822971091264876e-05, "metric_expression": "11.35549", "metric_symbol": "s", "metric_value": 11.355485166124788, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 11.1547, "setup": "domintri", "side": 11.355485166124788, "solution_path": "data/solutions/generated/domintri_023_7b6e8b12db0049b9.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7b6e8b12db0049b9.svg", "tolerance": 1e-08, "verified": true} +{"case": "domintri@24", "density": 0.7994546814908398, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "friedman_metric_expression": "9+4/\u221a3 = 11.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@24", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "9+4/\u221a3 = 11.30940+", "metric_symbol": "s", "metric_value": 11.3094, "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "af99e7edd2e30109", "improvement": -0.46593782822515983, "max_boundary_excess": -2.650568564648374e-06, "max_pair_overlap_depth": -2.5771491973358707e-05, "metric_expression": "11.77534", "metric_symbol": "s", "metric_value": 11.77533782822516, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 11.3094, "setup": "domintri", "side": 11.77533782822516, "solution_path": "data/solutions/generated/domintri_024_af99e7edd2e30109.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/af99e7edd2e30109.svg", "tolerance": 1e-08, "verified": true} {"case": "hexincir@1", "density": 0.826977987261634, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "48f5aa37c90550c8", "improvement": -9.284285680699611e-06, "max_boundary_excess": -6.547655283739573e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "r", "metric_value": 1.0000092842856807, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "hexincir", "side": 2.0000185685713614, "solution_path": "data/solutions/generated/hexincir_001_48f5aa37c90550c8.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/48f5aa37c90550c8.svg", "tolerance": 1e-08, "verified": true} {"case": "hexincir@2", "density": 0.508894613048892, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "3b6bd2554e997adc", "improvement": -0.0008187982614582534, "max_boundary_excess": -1.4989872811899119e-06, "max_pair_overlap_depth": -3.954921521903687e-05, "metric_expression": "1.80282", "metric_symbol": "r", "metric_value": 1.8028187982614583, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.802, "setup": "hexincir", "side": 3.6056375965229166, "solution_path": "data/solutions/generated/hexincir_002_3b6bd2554e997adc.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b6bd2554e997adc.svg", "tolerance": 1e-08, "verified": true} {"case": "hexincir@3", "density": 0.6202101203168955, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@3", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "194e619a74e29452", "improvement": -5.624955299809997e-05, "max_boundary_excess": -9.970405754344824e-06, "max_pair_overlap_depth": -7.230141190991447e-05, "metric_expression": "2.00006", "metric_symbol": "r", "metric_value": 2.000056249552998, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "hexincir", "side": 4.000112499105996, "solution_path": "data/solutions/generated/hexincir_003_194e619a74e29452.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/194e619a74e29452.svg", "tolerance": 1e-08, "verified": true} @@ -158,6 +174,7 @@ {"case": "hexincir@18", "density": 0.7834006630179079, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.35889, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@18", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "12eaac899664a007", "improvement": -0.0001945423028058002, "max_boundary_excess": -4.696366953105269e-06, "max_pair_overlap_depth": -1.0490734119961154e-05, "metric_expression": "4.35908", "metric_symbol": "r", "metric_value": 4.3590845423028055, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.35889, "setup": "hexincir", "side": 8.718169084605611, "solution_path": "data/solutions/generated/hexincir_018_12eaac899664a007.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/12eaac899664a007.svg", "tolerance": 1e-08, "verified": true} {"case": "hexincir@19", "density": 0.8269599994475847, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.35889, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@19", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "b4bf200670caf09c", "improvement": -9.681979153608467e-05, "max_boundary_excess": -5.636539265552187e-06, "max_pair_overlap_depth": -6.973398227638761e-06, "metric_expression": "4.35899", "metric_symbol": "r", "metric_value": 4.358986819791536, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.35889, "setup": "hexincir", "side": 8.717973639583072, "solution_path": "data/solutions/generated/hexincir_019_b4bf200670caf09c.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4bf200670caf09c.svg", "tolerance": 1e-08, "verified": true} {"case": "hexincir@20", "density": 0.7723857667872704, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.62598+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.62598, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "4.62598+", "metric_symbol": "r", "metric_value": 4.62598, "reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "30108dc5d1ea9a14", "improvement": -0.0015460646281777457, "max_boundary_excess": -1.8288872105642895e-06, "max_pair_overlap_depth": -4.792351042670617e-06, "metric_expression": "4.62753", "metric_symbol": "r", "metric_value": 4.627526064628178, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.62598, "setup": "hexincir", "side": 9.255052129256356, "solution_path": "data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/30108dc5d1ea9a14.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexincir@21", "density": 0.7917677222663352, "friedman_analytical_or_proved": false, "friedman_credit": "Enea Victor", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "friedman_metric_expression": "4.68339+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.68339, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@21", "credit": "Enea Victor", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "4.68339+", "metric_symbol": "r", "metric_value": 4.68339, "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "49a047c29bb184c3", "improvement": -1.5457789629635954e-05, "max_boundary_excess": -4.498160996568856e-06, "max_pair_overlap_depth": -3.8704072840012316e-06, "metric_expression": "4.68341", "metric_symbol": "r", "metric_value": 4.68340545778963, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.68339, "setup": "hexincir", "side": 9.36681091557926, "solution_path": "data/solutions/generated/hexincir_021_49a047c29bb184c3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/49a047c29bb184c3.svg", "tolerance": 1e-08, "verified": true} {"case": "hexindom@1", "density": 0.433010701548144, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "\u221a3 = 1.73205+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73205, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@1", "credit": "Trivial", "date": "", "family_updated": "4/6/26", "metric_expression": "\u221a3 = 1.73205+", "metric_symbol": "s", "metric_value": 1.73205, "reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "899222ca3c83cd8e", "improvement": -4.8082708896668436e-06, "max_boundary_excess": -1.0003297862271054e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.73205", "metric_symbol": "s", "metric_value": 1.7320548082708898, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.73205, "setup": "hexindom", "side": 3.4641096165417795, "solution_path": "data/solutions/generated/hexindom_001_899222ca3c83cd8e.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/899222ca3c83cd8e.svg", "tolerance": 1e-08, "verified": true} {"case": "hexindom@2", "density": 0.7237057542591544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "1.8946+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8946, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@2", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/6/26", "metric_expression": "1.8946+", "metric_symbol": "s", "metric_value": 1.8946, "reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "419ae881803808e0", "improvement": -0.00011952413629479075, "max_boundary_excess": -6.154031481298006e-06, "max_pair_overlap_depth": -4.420983116036614e-05, "metric_expression": "1.89472", "metric_symbol": "s", "metric_value": 1.8947195241362949, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.8946, "setup": "hexindom", "side": 3.7894390482725897, "solution_path": "data/solutions/generated/hexindom_002_419ae881803808e0.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/419ae881803808e0.svg", "tolerance": 1e-08, "verified": true} {"case": "hexindom@3", "density": 0.6059845041872388, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "6\u20132\u221a3 = 2.53589+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.53589, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/6/26", "metric_expression": "6\u20132\u221a3 = 2.53589+", "metric_symbol": "s", "metric_value": 2.53589, "reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "b8984cccc8c8714d", "improvement": -6.074031198854968e-05, "max_boundary_excess": -1.3815485928603266e-06, "max_pair_overlap_depth": -3.5690372763075295e-05, "metric_expression": "2.53595", "metric_symbol": "s", "metric_value": 2.5359507403119887, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.53589, "setup": "hexindom", "side": 5.0719014806239775, "solution_path": "data/solutions/generated/hexindom_003_b8984cccc8c8714d.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b8984cccc8c8714d.svg", "tolerance": 1e-08, "verified": true} @@ -198,6 +215,17 @@ {"case": "hexinhex@18", "density": 0.8437116836701195, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@18", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "4/15/26", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "e320d39029a817c1", "improvement": -0.0009070314872570151, "max_boundary_excess": 1.0443685916789865e-09, "max_pair_overlap_depth": -3.080790913889686e-05, "metric_expression": "4.61891", "metric_symbol": "s", "metric_value": 4.618907031487257, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.618, "setup": "hexinhex", "side": 4.618907031487257, "solution_path": "data/solutions/generated/hexinhex_018_e320d39029a817c1.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e320d39029a817c1.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinhex@19", "density": 0.8905854861904853, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@19", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "4/15/26", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4b11a1a09f2a5b70", "improvement": -0.0009046166982376036, "max_boundary_excess": -8.772589960788204e-06, "max_pair_overlap_depth": -3.612300978728111e-05, "metric_expression": "4.61890", "metric_symbol": "s", "metric_value": 4.618904616698238, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.618, "setup": "hexinhex", "side": 4.618904616698238, "solution_path": "data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4b11a1a09f2a5b70.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinhex@20", "density": 0.7999496824068819, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@20", "credit": "Trivial", "date": "", "family_updated": "4/15/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "20-21. | | s = 5 | Trivial. | |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "2830e2dec38749ef", "improvement": -0.00015724989644283482, "max_boundary_excess": -5.445035556179186e-06, "max_pair_overlap_depth": -1.6551811964360397e-06, "metric_expression": "5.00016", "metric_symbol": "s", "metric_value": 5.000157249896443, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000157249896443, "solution_path": "data/solutions/generated/hexinhex_020_2830e2dec38749ef.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2830e2dec38749ef.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@21", "density": 0.8399773177134815, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@21", "credit": "Trivial", "date": "", "family_updated": "4/15/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "20-21. | | s = 5 | Trivial. | |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4a431b677be571c9", "improvement": -6.750817229672634e-05, "max_boundary_excess": -1.5389132812752791e-06, "max_pair_overlap_depth": -3.519050301936666e-06, "metric_expression": "5.00007", "metric_symbol": "s", "metric_value": 5.000067508172297, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000067508172297, "solution_path": "data/solutions/generated/hexinhex_021_4a431b677be571c9.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a431b677be571c9.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@22", "density": 0.7873804951730353, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "friedman_metric_expression": "(39+8\u221a3)/10 = 5.285+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.285, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@22", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "4/15/26", "metric_expression": "(39+8\u221a3)/10 = 5.285+", "metric_symbol": "s", "metric_value": 5.285, "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "003a713177cb171c", "improvement": -0.0009008698048820207, "max_boundary_excess": -4.575542655386671e-06, "max_pair_overlap_depth": -1.0001604064946434e-05, "metric_expression": "5.28590", "metric_symbol": "s", "metric_value": 5.285900869804882, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.285, "setup": "hexinhex", "side": 5.285900869804882, "solution_path": "data/solutions/generated/hexinhex_022_003a713177cb171c.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/003a713177cb171c.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@23", "density": 0.7758097131766583, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "friedman_metric_expression": "5.400+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@23", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "4/15/26", "metric_expression": "5.400+", "metric_symbol": "s", "metric_value": 5.4, "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4a3a3fd07554d52b", "improvement": -0.04485491175923784, "max_boundary_excess": -2.3299387411464314e-06, "max_pair_overlap_depth": -5.1241164786830495e-05, "metric_expression": "5.44485", "metric_symbol": "s", "metric_value": 5.444854911759238, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.4, "setup": "hexinhex", "side": 5.444854911759238, "solution_path": "data/solutions/generated/hexinhex_023_4a3a3fd07554d52b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a3a3fd07554d52b.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@24", "density": 0.797738483588153, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "friedman_metric_expression": "19\u221a3/6 = 5.484+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.484, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@24", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "4/15/26", "metric_expression": "19\u221a3/6 = 5.484+", "metric_symbol": "s", "metric_value": 5.484, "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "c96649ff013a9455", "improvement": -0.00098379990619879, "max_boundary_excess": -9.588312731744032e-06, "max_pair_overlap_depth": -4.485524381903083e-05, "metric_expression": "5.48498", "metric_symbol": "s", "metric_value": 5.484983799906199, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.484, "setup": "hexinhex", "side": 5.484983799906199, "solution_path": "data/solutions/generated/hexinhex_024_c96649ff013a9455.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c96649ff013a9455.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@25", "density": 0.7898226009433017, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "friedman_metric_expression": "5.62390+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.6239, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@25", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "4/15/26", "metric_expression": "5.62390+", "metric_symbol": "s", "metric_value": 5.6239, "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4ac680367830872b", "improvement": -0.002171223468265815, "max_boundary_excess": -1.8833146044517865e-07, "max_pair_overlap_depth": -2.7316686140865798e-05, "metric_expression": "5.62607", "metric_symbol": "s", "metric_value": 5.626071223468266, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.6239, "setup": "hexinhex", "side": 5.626071223468266, "solution_path": "data/solutions/generated/hexinhex_025_4ac680367830872b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4ac680367830872b.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@26", "density": 0.7947867651922452, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "friedman_metric_expression": "5.70972+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.70972, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@26", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "4/15/26", "metric_expression": "5.70972+", "metric_symbol": "s", "metric_value": 5.70972, "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "0a420d645748969b", "improvement": -0.009823411865984788, "max_boundary_excess": -9.859507481158646e-07, "max_pair_overlap_depth": -3.367354169281356e-05, "metric_expression": "5.71954", "metric_symbol": "s", "metric_value": 5.719543411865985, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.70972, "setup": "hexinhex", "side": 5.719543411865985, "solution_path": "data/solutions/generated/hexinhex_026_0a420d645748969b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0a420d645748969b.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@27", "density": 0.82621496088318, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "friedman_metric_expression": "5.71415+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.71415, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@27", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "4/15/26", "metric_expression": "5.71415+", "metric_symbol": "s", "metric_value": 5.71415, "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4e9628a9f49def85", "improvement": -0.0024177469948583052, "max_boundary_excess": -4.56387472302006e-06, "max_pair_overlap_depth": -5.6693937127594296e-05, "metric_expression": "5.71657", "metric_symbol": "s", "metric_value": 5.716567746994858, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.71415, "setup": "hexinhex", "side": 5.716567746994858, "solution_path": "data/solutions/generated/hexinhex_027_4e9628a9f49def85.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4e9628a9f49def85.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@28", "density": 0.7877627529922571, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "friedman_metric_expression": "5.90893+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.90893, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@28", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "4/15/26", "metric_expression": "5.90893+", "metric_symbol": "s", "metric_value": 5.90893, "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "59dc7d7850663cbb", "improvement": -0.052923423059089814, "max_boundary_excess": -8.181764566584125e-06, "max_pair_overlap_depth": -1.7101544528386192e-05, "metric_expression": "5.96185", "metric_symbol": "s", "metric_value": 5.96185342305909, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.90893, "setup": "hexinhex", "side": 5.96185342305909, "solution_path": "data/solutions/generated/hexinhex_028_59dc7d7850663cbb.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/59dc7d7850663cbb.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@29", "density": 0.8055194808067645, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@29", "credit": "Trivial", "date": "", "family_updated": "4/15/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "dba25a591b8992bc", "improvement": -0.00013435185279675466, "max_boundary_excess": -5.231638156342025e-06, "max_pair_overlap_depth": -6.307567709251671e-06, "metric_expression": "6.00013", "metric_symbol": "s", "metric_value": 6.000134351852797, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000134351852797, "solution_path": "data/solutions/generated/hexinhex_029_dba25a591b8992bc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dba25a591b8992bc.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@30", "density": 0.8333115277207207, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@30", "credit": "Trivial", "date": "", "family_updated": "4/15/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "100db5f9f28894cc", "improvement": -7.850174601031767e-05, "max_boundary_excess": -3.7272811687230685e-07, "max_pair_overlap_depth": -4.232627726974414e-06, "metric_expression": "6.00008", "metric_symbol": "s", "metric_value": 6.00007850174601, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.00007850174601, "solution_path": "data/solutions/generated/hexinhex_030_100db5f9f28894cc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/100db5f9f28894cc.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinhex@31", "density": 0.8610814974425702, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@31", "credit": "Trivial", "date": "", "family_updated": "4/15/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "d503e2b08764a35e", "improvement": -0.0001031728611780025, "max_boundary_excess": -1.0312532034243658e-06, "max_pair_overlap_depth": -8.80446118189937e-06, "metric_expression": "6.00010", "metric_symbol": "s", "metric_value": 6.000103172861178, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000103172861178, "solution_path": "data/solutions/generated/hexinhex_031_d503e2b08764a35e.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d503e2b08764a35e.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinsqu@1", "density": 0.6961402306608654, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.931, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "metric_symbol": "s", "metric_value": 1.931, "reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "1cfff36edc20de72", "improvement": -0.000868569514983486, "max_boundary_excess": -1.8875760125229138e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.93187", "metric_symbol": "s", "metric_value": 1.9318685695149835, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.931, "setup": "hexinsqu", "side": 1.9318685695149835, "solution_path": "data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1cfff36edc20de72.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinsqu@2", "density": 0.5214616218348717, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.156, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "metric_symbol": "s", "metric_value": 3.156, "reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "ff43d04cda84c856", "improvement": -0.0006742348964126066, "max_boundary_excess": -1.2405599436706566e-05, "max_pair_overlap_depth": -1.629836664562411e-05, "metric_expression": "3.15667", "metric_symbol": "s", "metric_value": 3.1566742348964127, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.156, "setup": "hexinsqu", "side": 3.1566742348964127, "solution_path": "data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ff43d04cda84c856.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinsqu@3", "density": 0.6391474518535116, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.491, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "4/28/26", "metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "metric_symbol": "s", "metric_value": 3.491, "reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "9525d376eafe3c9c", "improvement": -0.0010949178753740796, "max_boundary_excess": -2.084317521962771e-06, "max_pair_overlap_depth": -8.912711465047796e-05, "metric_expression": "3.49209", "metric_symbol": "s", "metric_value": 3.492094917875374, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.491, "setup": "hexinsqu", "side": 3.492094917875374, "solution_path": "data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9525d376eafe3c9c.svg", "tolerance": 1e-08, "verified": true} @@ -218,6 +246,11 @@ {"case": "hexinsqu@18", "density": 0.7508119114984774, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.702, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@18", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "metric_symbol": "s", "metric_value": 7.702, "reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "04bf4ecb433a40bc", "improvement": -0.1901734023169297, "max_boundary_excess": -6.471545418890209e-06, "max_pair_overlap_depth": -3.179483178339382e-05, "metric_expression": "7.89217", "metric_symbol": "s", "metric_value": 7.89217340231693, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.702, "setup": "hexinsqu", "side": 7.89217340231693, "solution_path": "data/solutions/generated/hexinsqu_018_04bf4ecb433a40bc.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/04bf4ecb433a40bc.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinsqu@19", "density": 0.7859807737367643, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.924, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@19", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "metric_symbol": "s", "metric_value": 7.924, "reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "10d9f5dde53d25ba", "improvement": -0.0009545892016307178, "max_boundary_excess": -2.893895229540556e-06, "max_pair_overlap_depth": -3.6221248433054853e-05, "metric_expression": "7.92495", "metric_symbol": "s", "metric_value": 7.924954589201631, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.924, "setup": "hexinsqu", "side": 7.924954589201631, "solution_path": "data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/10d9f5dde53d25ba.svg", "tolerance": 1e-08, "verified": true} {"case": "hexinsqu@20", "density": 0.8222377903171622, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.948, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "metric_symbol": "s", "metric_value": 7.948, "reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "3d530c0ac6e7e3b1", "improvement": -0.0015441274741458955, "max_boundary_excess": -8.121785608292394e-06, "max_pair_overlap_depth": -4.480534023287852e-05, "metric_expression": "7.94954", "metric_symbol": "s", "metric_value": 7.949544127474146, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.948, "setup": "hexinsqu", "side": 7.949544127474146, "solution_path": "data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3d530c0ac6e7e3b1.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinsqu@21", "density": 0.7762795555424945, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "friedman_metric_expression": "8.381+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.381, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@21", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "8.381+", "metric_symbol": "s", "metric_value": 8.381, "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "5d369a2740fde606", "improvement": -0.002522153681731254, "max_boundary_excess": -4.85221561134309e-06, "max_pair_overlap_depth": -3.989714052887727e-05, "metric_expression": "8.38352", "metric_symbol": "s", "metric_value": 8.383522153681731, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.381, "setup": "hexinsqu", "side": 8.383522153681731, "solution_path": "data/solutions/generated/hexinsqu_021_5d369a2740fde606.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5d369a2740fde606.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinsqu@22", "density": 0.7770815845496467, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "friedman_metric_expression": "8.568+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.568, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "8.568+", "metric_symbol": "s", "metric_value": 8.568, "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "2f0b0033f0c66708", "improvement": -0.008379204155273712, "max_boundary_excess": -2.913077650512531e-06, "max_pair_overlap_depth": -1.9097490104869053e-05, "metric_expression": "8.57638", "metric_symbol": "s", "metric_value": 8.576379204155273, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.568, "setup": "hexinsqu", "side": 8.576379204155273, "solution_path": "data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2f0b0033f0c66708.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinsqu@23", "density": 0.7967168154089415, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "friedman_metric_expression": "5\u221a3 = 8.660+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.66, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@23", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "5\u221a3 = 8.660+", "metric_symbol": "s", "metric_value": 8.66, "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "31cc17034bd25d7b", "improvement": -0.0003983679346664104, "max_boundary_excess": -5.345963802137002e-06, "max_pair_overlap_depth": -2.1349502021816846e-07, "metric_expression": "8.66040", "metric_symbol": "s", "metric_value": 8.660398367934667, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.66, "setup": "hexinsqu", "side": 8.660398367934667, "solution_path": "data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/31cc17034bd25d7b.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinsqu@24", "density": 0.8058676683577897, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "friedman_metric_expression": "8.795+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.795, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@24", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "8.795+", "metric_symbol": "s", "metric_value": 8.795, "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "941fbce4f50492c6", "improvement": -0.0012932219182459903, "max_boundary_excess": -1.0969884292392119e-07, "max_pair_overlap_depth": -1.611027152126354e-05, "metric_expression": "8.79629", "metric_symbol": "s", "metric_value": 8.796293221918246, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.795, "setup": "hexinsqu", "side": 8.796293221918246, "solution_path": "data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/941fbce4f50492c6.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexinsqu@25", "density": 0.7836571783494045, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "friedman_metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.065, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@25", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "metric_symbol": "s", "metric_value": 9.065, "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "d89d09725d796421", "improvement": -0.03901342531098173, "max_boundary_excess": -8.46381858025372e-06, "max_pair_overlap_depth": -3.4782095370111676e-05, "metric_expression": "9.10401", "metric_symbol": "s", "metric_value": 9.104013425310981, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.065, "setup": "hexinsqu", "side": 9.104013425310981, "solution_path": "data/solutions/generated/hexinsqu_025_d89d09725d796421.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d89d09725d796421.svg", "tolerance": 1e-08, "verified": true} {"case": "hexintri@1", "density": 0.6666490309389511, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@1", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "c2fff75544b88239", "improvement": -3.9681174644368156e-05, "max_boundary_excess": -7.67464904574664e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.00004", "metric_symbol": "s", "metric_value": 3.0000396811746444, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.0, "setup": "hexintri", "side": 3.0000396811746444, "solution_path": "data/solutions/generated/hexintri_001_c2fff75544b88239.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c2fff75544b88239.svg", "tolerance": 1e-08, "verified": true} {"case": "hexintri@2", "density": 0.4799802064426444, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@2", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "b77426ecb97f3ce6", "improvement": -0.00010309463302426991, "max_boundary_excess": -2.3591084715906373e-06, "max_pair_overlap_depth": -4.2178351187804886e-05, "metric_expression": "5.00010", "metric_symbol": "s", "metric_value": 5.000103094633024, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000103094633024, "solution_path": "data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b77426ecb97f3ce6.svg", "tolerance": 1e-08, "verified": true} {"case": "hexintri@3", "density": 0.7199659208954582, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@3", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "748bfe1ef47ea18c", "improvement": -0.00011833442488207169, "max_boundary_excess": -2.3474135610435156e-06, "max_pair_overlap_depth": -4.4955482604913666e-05, "metric_expression": "5.00012", "metric_symbol": "s", "metric_value": 5.000118334424882, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000118334424882, "solution_path": "data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/748bfe1ef47ea18c.svg", "tolerance": 1e-08, "verified": true} @@ -238,6 +271,7 @@ {"case": "hexintri@18", "density": 0.7507767554452202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@18", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "8f10cd5e01be9029", "improvement": 0.0062092209316340075, "max_boundary_excess": -6.734105056962567e-06, "max_pair_overlap_depth": -5.8920104462956147e-05, "metric_expression": "11.99379", "metric_symbol": "s", "metric_value": 11.993790779068366, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 11.993790779068366, "solution_path": "data/solutions/generated/hexintri_018_8f10cd5e01be9029.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8f10cd5e01be9029.svg", "tolerance": 1e-08, "verified": true} {"case": "hexintri@19", "density": 0.7754553480185566, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@19", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "43012deed1bb1dba", "improvement": -0.12478448660763952, "max_boundary_excess": -5.837329751695746e-06, "max_pair_overlap_depth": -3.825923946865206e-05, "metric_expression": "12.12478", "metric_symbol": "s", "metric_value": 12.12478448660764, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 12.12478448660764, "solution_path": "data/solutions/generated/hexintri_019_43012deed1bb1dba.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/43012deed1bb1dba.svg", "tolerance": 1e-08, "verified": true} {"case": "hexintri@20", "density": 0.8162942117377381, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.1243, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@20", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f59179c5b6665dc4", "improvement": -0.00029566549525483765, "max_boundary_excess": -6.116403950810266e-06, "max_pair_overlap_depth": -3.364591626842106e-05, "metric_expression": "12.12460", "metric_symbol": "s", "metric_value": 12.124595665495255, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.1243, "setup": "hexintri", "side": 12.124595665495255, "solution_path": "data/solutions/generated/hexintri_020_f59179c5b6665dc4.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f59179c5b6665dc4.svg", "tolerance": 1e-08, "verified": true} +{"case": "hexintri@21", "density": 0.8571035425372456, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.1243, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@21", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "6cf726ac83ba7d7f", "improvement": -0.00033371669977810825, "max_boundary_excess": -3.7607980864287318e-06, "max_pair_overlap_depth": -2.977721456209892e-05, "metric_expression": "12.12463", "metric_symbol": "s", "metric_value": 12.124633716699778, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.1243, "setup": "hexintri", "side": 12.124633716699778, "solution_path": "data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6cf726ac83ba7d7f.svg", "tolerance": 1e-08, "verified": true} {"case": "octinoct@1", "density": 0.9999940796878448, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@1", "credit": "Trivial", "date": "", "family_updated": "3/27/26", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 1 | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "13c63959e19cfeb5", "improvement": -2.96016922152198e-06, "max_boundary_excess": -2.1903479056983753e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_symbol": "s", "metric_value": 1.0000029601692215, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "octinoct", "side": 1.0000029601692215, "solution_path": "data/solutions/generated/octinoct_001_13c63959e19cfeb5.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/13c63959e19cfeb5.svg", "tolerance": 1e-08, "verified": true} {"case": "octinoct@2", "density": 0.4999889107582135, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@2", "credit": "Trivial", "date": "", "family_updated": "3/27/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "937fb450c622d9b9", "improvement": -2.2178852493670576e-05, "max_boundary_excess": -5.909847599495863e-06, "max_pair_overlap_depth": -3.0343321494846753e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.0000221788524937, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "octinoct", "side": 2.0000221788524937, "solution_path": "data/solutions/generated/octinoct_002_937fb450c622d9b9.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/937fb450c622d9b9.svg", "tolerance": 1e-08, "verified": true} {"case": "octinoct@3", "density": 0.6361550822369931, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5\u20132\u221a2 = 2.17157+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.17157, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@3", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5\u20132\u221a2 = 2.17157+", "metric_symbol": "s", "metric_value": 2.17157, "reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4cb37df94277ed6e", "improvement": -2.6468916854760494e-05, "max_boundary_excess": -4.359798521217012e-07, "max_pair_overlap_depth": -2.9093807346031175e-05, "metric_expression": "2.17160", "metric_symbol": "s", "metric_value": 2.1715964689168548, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.17157, "setup": "octinoct", "side": 2.1715964689168548, "solution_path": "data/solutions/generated/octinoct_003_4cb37df94277ed6e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4cb37df94277ed6e.svg", "tolerance": 1e-08, "verified": true} @@ -258,6 +292,16 @@ {"case": "octinoct@18", "density": 0.7629999765077309, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.85717+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.85717, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "4.85717+", "metric_symbol": "s", "metric_value": 4.85717, "reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "46f5ac176d150ffa", "improvement": 0.00010416375427002578, "max_boundary_excess": -8.225773906749903e-06, "max_pair_overlap_depth": -2.521618462036912e-05, "metric_expression": "4.85707", "metric_symbol": "s", "metric_value": 4.85706583624573, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.85717, "setup": "octinoct", "side": 4.85706583624573, "solution_path": "data/solutions/generated/octinoct_018_46f5ac176d150ffa.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/46f5ac176d150ffa.svg", "tolerance": 1e-08, "verified": true} {"case": "octinoct@19", "density": 0.7795195170060211, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.93586+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93586, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "4.93586+", "metric_symbol": "s", "metric_value": 4.93586, "reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4a7169be4bda1825", "improvement": -0.0011420082689239663, "max_boundary_excess": -1.1928573301213418e-05, "max_pair_overlap_depth": -1.491417372267989e-06, "metric_expression": "4.93700", "metric_symbol": "s", "metric_value": 4.937002008268924, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.93586, "setup": "octinoct", "side": 4.937002008268924, "solution_path": "data/solutions/generated/octinoct_019_4a7169be4bda1825.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a7169be4bda1825.svg", "tolerance": 1e-08, "verified": true} {"case": "octinoct@20", "density": 0.778654925537014, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5.06781+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.06781, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.06781+", "metric_symbol": "s", "metric_value": 5.06781, "reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "ef9ffbe57f51321a", "improvement": -0.0002585475900360734, "max_boundary_excess": -5.202696065204785e-06, "max_pair_overlap_depth": -3.692189855719619e-05, "metric_expression": "5.06807", "metric_symbol": "s", "metric_value": 5.068068547590036, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.06781, "setup": "octinoct", "side": 5.068068547590036, "solution_path": "data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ef9ffbe57f51321a.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@21", "density": 0.7774838310416734, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "friedman_metric_expression": "5.19715+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.19715, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.19715+", "metric_symbol": "s", "metric_value": 5.19715, "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "92c4bcf9428983c2", "improvement": 1.540400287325383e-05, "max_boundary_excess": -7.1696825424876755e-06, "max_pair_overlap_depth": -2.317393259165801e-05, "metric_expression": "5.19713", "metric_symbol": "s", "metric_value": 5.1971345959971265, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.19715, "setup": "octinoct", "side": 5.1971345959971265, "solution_path": "data/solutions/generated/octinoct_021_92c4bcf9428983c2.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92c4bcf9428983c2.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@22", "density": 0.7663269933124698, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "friedman_metric_expression": "5.35750+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.3575, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.35750+", "metric_symbol": "s", "metric_value": 5.3575, "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "b8f2befaa2d4a75e", "improvement": -0.0005193617687213603, "max_boundary_excess": -4.99203724676962e-06, "max_pair_overlap_depth": -1.57400449714018e-05, "metric_expression": "5.35802", "metric_symbol": "s", "metric_value": 5.358019361768721, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.3575, "setup": "octinoct", "side": 5.358019361768721, "solution_path": "data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b8f2befaa2d4a75e.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@23", "density": 0.7845835529808874, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "friedman_metric_expression": "5.41440+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4144, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.41440+", "metric_symbol": "s", "metric_value": 5.4144, "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "d6528e8801e36ce0", "improvement": 7.503853147827755e-05, "max_boundary_excess": -3.3646686331794102e-06, "max_pair_overlap_depth": -4.536567227386712e-05, "metric_expression": "5.41432", "metric_symbol": "s", "metric_value": 5.414324961468521, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.4144, "setup": "octinoct", "side": 5.414324961468521, "solution_path": "data/solutions/generated/octinoct_023_d6528e8801e36ce0.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d6528e8801e36ce0.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@24", "density": 0.777859618157, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "friedman_metric_expression": "5.55464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.55464, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.55464+", "metric_symbol": "s", "metric_value": 5.55464, "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "a34ac6a3c52f70df", "improvement": 1.1631965286973411e-05, "max_boundary_excess": -7.721783559078116e-06, "max_pair_overlap_depth": -2.4974900467711336e-05, "metric_expression": "5.55463", "metric_symbol": "s", "metric_value": 5.554628368034713, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.55464, "setup": "octinoct", "side": 5.554628368034713, "solution_path": "data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a34ac6a3c52f70df.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@25", "density": 0.7805673327264805, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "friedman_metric_expression": "5.65593+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.65593, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.65593+", "metric_symbol": "s", "metric_value": 5.65593, "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "113492960b7e7dce", "improvement": -0.003397389940226425, "max_boundary_excess": -6.281212189125961e-06, "max_pair_overlap_depth": -2.6024797291412938e-05, "metric_expression": "5.65933", "metric_symbol": "s", "metric_value": 5.659327389940226, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.65593, "setup": "octinoct", "side": 5.659327389940226, "solution_path": "data/solutions/generated/octinoct_025_113492960b7e7dce.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/113492960b7e7dce.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@26", "density": 0.7881657239941322, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "friedman_metric_expression": "5.73940+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.7394, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.73940+", "metric_symbol": "s", "metric_value": 5.7394, "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "581188c4895e4037", "improvement": -0.004116881359766289, "max_boundary_excess": -6.43705423351296e-06, "max_pair_overlap_depth": -2.686615288460814e-05, "metric_expression": "5.74352", "metric_symbol": "s", "metric_value": 5.743516881359766, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.7394, "setup": "octinoct", "side": 5.743516881359766, "solution_path": "data/solutions/generated/octinoct_026_581188c4895e4037.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/581188c4895e4037.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@27", "density": 0.7989711846148311, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "friedman_metric_expression": "5.81238+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.81238, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.81238+", "metric_symbol": "s", "metric_value": 5.81238, "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "25c7f85bc0b15209", "improvement": -0.0008341744667159645, "max_boundary_excess": -3.851030556516347e-06, "max_pair_overlap_depth": -2.4661009629944886e-05, "metric_expression": "5.81321", "metric_symbol": "s", "metric_value": 5.813214174466716, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.81238, "setup": "octinoct", "side": 5.813214174466716, "solution_path": "data/solutions/generated/octinoct_027_25c7f85bc0b15209.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/25c7f85bc0b15209.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@28", "density": 0.8242204012359605, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "friedman_metric_expression": "3+2\u221a2 = 5.82842+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.82842, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "3+2\u221a2 = 5.82842+", "metric_symbol": "s", "metric_value": 5.82842, "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "f8d9c8a9f9a38d45", "improvement": -8.71778893589692e-05, "max_boundary_excess": -6.739062384519148e-06, "max_pair_overlap_depth": -9.673739088000843e-06, "metric_expression": "5.82851", "metric_symbol": "s", "metric_value": 5.828507177889359, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.82842, "setup": "octinoct", "side": 5.828507177889359, "solution_path": "data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f8d9c8a9f9a38d45.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@29", "density": 0.7902111886471865, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "friedman_metric_expression": "6.05746+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.05746, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "6.05746+", "metric_symbol": "s", "metric_value": 6.05746, "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "30789c6bb8fd99b7", "improvement": -0.0005140918720876186, "max_boundary_excess": -7.805265150873157e-06, "max_pair_overlap_depth": -5.6301265520808386e-05, "metric_expression": "6.05797", "metric_symbol": "s", "metric_value": 6.0579740918720875, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.05746, "setup": "octinoct", "side": 6.0579740918720875, "solution_path": "data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/30789c6bb8fd99b7.svg", "tolerance": 1e-08, "verified": true} +{"case": "octinoct@30", "density": 0.7919434557655346, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "friedman_metric_expression": "6.15432+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.15432, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "6.15432+", "metric_symbol": "s", "metric_value": 6.15432, "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "1a16dc8a4d741008", "improvement": -0.00047426130353134255, "max_boundary_excess": -1.1243912272535679e-05, "max_pair_overlap_depth": -2.8046648627544357e-05, "metric_expression": "6.15479", "metric_symbol": "s", "metric_value": 6.154794261303532, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.15432, "setup": "octinoct", "side": 6.154794261303532, "solution_path": "data/solutions/generated/octinoct_030_1a16dc8a4d741008.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1a16dc8a4d741008.svg", "tolerance": 1e-08, "verified": true} {"case": "penincir@1", "density": 0.7568185573097284, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.86065, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@1", "credit": "Trivial", "date": "", "family_updated": "4/13/26", "metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "metric_symbol": "r", "metric_value": 0.86065, "reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "ca75a5cd7cad481c", "improvement": 0.009994599443903796, "max_boundary_excess": -2.0926430426282394e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.85066", "metric_symbol": "r", "metric_value": 0.8506554005560962, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.86065, "setup": "penincir", "side": 1.7013108011121925, "solution_path": "data/solutions/generated/penincir_001_ca75a5cd7cad481c.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ca75a5cd7cad481c.svg", "tolerance": 1e-08, "verified": true} {"case": "penincir@2", "density": 0.462509898701161, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.53884, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@2", "credit": "Trivial", "date": "", "family_updated": "4/13/26", "metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "metric_symbol": "r", "metric_value": 1.53884, "reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "44da10d1d5897aae", "improvement": -3.743542237466535e-05, "max_boundary_excess": -8.684702690331392e-08, "max_pair_overlap_depth": -5.994543612077171e-05, "metric_expression": "1.53888", "metric_symbol": "r", "metric_value": 1.5388774354223747, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.53884, "setup": "penincir", "side": 3.0777548708447493, "solution_path": "data/solutions/generated/penincir_002_44da10d1d5897aae.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/44da10d1d5897aae.svg", "tolerance": 1e-08, "verified": true} {"case": "penincir@3", "density": 0.6275054691586099, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "(1+\u221a5)/2 = 1.61803+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.61803, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@3", "credit": "Trivial", "date": "", "family_updated": "4/13/26", "metric_expression": "(1+\u221a5)/2 = 1.61803+", "metric_symbol": "r", "metric_value": 1.61803, "reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "350d35e2110a508b", "improvement": -5.532631868709892e-05, "max_boundary_excess": -4.919906156253262e-06, "max_pair_overlap_depth": -5.073652219536114e-05, "metric_expression": "1.61809", "metric_symbol": "r", "metric_value": 1.6180853263186872, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.61803, "setup": "penincir", "side": 3.2361706526373744, "solution_path": "data/solutions/generated/penincir_003_350d35e2110a508b.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/350d35e2110a508b.svg", "tolerance": 1e-08, "verified": true} @@ -278,6 +322,7 @@ {"case": "penincir@18", "density": 0.7533573813986445, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.62080+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.6208, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.62080+", "metric_symbol": "r", "metric_value": 3.6208, "reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "767a627015948f32", "improvement": 0.00349375267338381, "max_boundary_excess": -3.7774333678797234e-06, "max_pair_overlap_depth": -3.109065453799076e-05, "metric_expression": "3.61731", "metric_symbol": "r", "metric_value": 3.617306247326616, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.6208, "setup": "penincir", "side": 7.234612494653232, "solution_path": "data/solutions/generated/penincir_018_767a627015948f32.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/767a627015948f32.svg", "tolerance": 1e-08, "verified": true} {"case": "penincir@19", "density": 0.771366675320165, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.67287+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.67287, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.67287+", "metric_symbol": "r", "metric_value": 3.67287, "reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "9d482c8012998879", "improvement": 8.154982387598153e-05, "max_boundary_excess": -3.817340790579493e-06, "max_pair_overlap_depth": -1.6517110137281854e-05, "metric_expression": "3.67279", "metric_symbol": "r", "metric_value": 3.672788450176124, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.67287, "setup": "penincir", "side": 7.345576900352248, "solution_path": "data/solutions/generated/penincir_019_9d482c8012998879.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9d482c8012998879.svg", "tolerance": 1e-08, "verified": true} {"case": "penincir@20", "density": 0.7575056542556782, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.80415+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.80415, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.80415+", "metric_symbol": "r", "metric_value": 3.80415, "reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "5271226652403829", "improvement": 0.0016291138375779113, "max_boundary_excess": -7.231424091092009e-06, "max_pair_overlap_depth": -3.071782635011289e-05, "metric_expression": "3.80252", "metric_symbol": "r", "metric_value": 3.802520886162422, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.80415, "setup": "penincir", "side": 7.605041772324844, "solution_path": "data/solutions/generated/penincir_020_5271226652403829.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5271226652403829.svg", "tolerance": 1e-08, "verified": true} +{"case": "penincir@21", "density": 0.7444892702855748, "friedman_analytical_or_proved": false, "friedman_credit": "Cyril Summerfield", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "friedman_metric_expression": "3.90735+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.90735, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@21", "credit": "Cyril Summerfield", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.90735+", "metric_symbol": "r", "metric_value": 3.90735, "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "b713bb4909b828e8", "improvement": -0.02298868203306892, "max_boundary_excess": -1.870622546595868e-05, "max_pair_overlap_depth": -5.364219534342851e-06, "metric_expression": "3.93034", "metric_symbol": "r", "metric_value": 3.930338682033069, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.90735, "setup": "penincir", "side": 7.860677364066138, "solution_path": "data/solutions/generated/penincir_021_b713bb4909b828e8.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b713bb4909b828e8.svg", "tolerance": 1e-08, "verified": true} {"case": "peninpen@1", "density": 0.9999780359352667, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b3173648630fcdeb", "improvement": -1.0982213277443975e-05, "max_boundary_excess": -6.256503348572871e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000109822132774, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "peninpen", "side": 1.0000109822132774, "solution_path": "data/solutions/generated/peninpen_001_b3173648630fcdeb.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b3173648630fcdeb.svg", "tolerance": 1e-08, "verified": true} {"case": "peninpen@2", "density": 0.4999891232484648, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "edac094186a54129", "improvement": -2.175385798786067e-05, "max_boundary_excess": -3.0537211348702708e-06, "max_pair_overlap_depth": -1.9731507571563167e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.000021753857988, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "peninpen", "side": 2.000021753857988, "solution_path": "data/solutions/generated/peninpen_002_edac094186a54129.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/edac094186a54129.svg", "tolerance": 1e-08, "verified": true} {"case": "peninpen@3", "density": 0.599978840427638, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a5 = 2.23606+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23606, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "\u221a5 = 2.23606+", "metric_symbol": "s", "metric_value": 2.23606, "reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "bf261a4dce178a90", "improvement": -4.7407077830463606e-05, "max_boundary_excess": -2.7662857614262655e-06, "max_pair_overlap_depth": -2.7755970794667603e-05, "metric_expression": "2.23611", "metric_symbol": "s", "metric_value": 2.2361074070778306, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.23606, "setup": "peninpen", "side": 2.2361074070778306, "solution_path": "data/solutions/generated/peninpen_003_bf261a4dce178a90.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bf261a4dce178a90.svg", "tolerance": 1e-08, "verified": true} @@ -298,6 +343,11 @@ {"case": "peninpen@18", "density": 0.7892194761771266, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.77541+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.77541, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.77541+", "metric_symbol": "s", "metric_value": 4.77541, "reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "9c442356ca78c3de", "improvement": -0.0002934971525236918, "max_boundary_excess": -3.1318004154280254e-06, "max_pair_overlap_depth": -1.258487199295999e-05, "metric_expression": "4.77570", "metric_symbol": "s", "metric_value": 4.775703497152524, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.77541, "setup": "peninpen", "side": 4.775703497152524, "solution_path": "data/solutions/generated/peninpen_018_9c442356ca78c3de.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9c442356ca78c3de.svg", "tolerance": 1e-08, "verified": true} {"case": "peninpen@19", "density": 0.7735353200149236, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.95269+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.95269, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.95269+", "metric_symbol": "s", "metric_value": 4.95269, "reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b5440311f7b9b10b", "improvement": -0.0033719480383975764, "max_boundary_excess": -3.8067945532274755e-06, "max_pair_overlap_depth": -5.844604614307913e-06, "metric_expression": "4.95606", "metric_symbol": "s", "metric_value": 4.956061948038397, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.95269, "setup": "peninpen", "side": 4.956061948038397, "solution_path": "data/solutions/generated/peninpen_019_b5440311f7b9b10b.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b5440311f7b9b10b.svg", "tolerance": 1e-08, "verified": true} {"case": "peninpen@20", "density": 0.7890584950748962, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.04154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.04154, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.04154+", "metric_symbol": "s", "metric_value": 5.04154, "reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "74f61b73dca76fef", "improvement": 0.0069930192193110585, "max_boundary_excess": -6.063547145356236e-06, "max_pair_overlap_depth": -1.8870971417950244e-05, "metric_expression": "5.03455", "metric_symbol": "s", "metric_value": 5.034546980780689, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.04154, "setup": "peninpen", "side": 5.034546980780689, "solution_path": "data/solutions/generated/peninpen_020_74f61b73dca76fef.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/74f61b73dca76fef.svg", "tolerance": 1e-08, "verified": true} +{"case": "peninpen@21", "density": 0.7872654636004235, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "friedman_metric_expression": "5.15948+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.15948, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.15948+", "metric_symbol": "s", "metric_value": 5.15948, "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "1c71a8b98efbf1a2", "improvement": -0.005266945011011437, "max_boundary_excess": -8.105180534871506e-06, "max_pair_overlap_depth": -1.0939088816552811e-05, "metric_expression": "5.16475", "metric_symbol": "s", "metric_value": 5.164746945011012, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.15948, "setup": "peninpen", "side": 5.164746945011012, "solution_path": "data/solutions/generated/peninpen_021_1c71a8b98efbf1a2.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1c71a8b98efbf1a2.svg", "tolerance": 1e-08, "verified": true} +{"case": "peninpen@22", "density": 0.7927891464448104, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "friedman_metric_expression": "5.26740+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.2674, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.26740+", "metric_symbol": "s", "metric_value": 5.2674, "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "07e217f200bb677e", "improvement": -0.0004389908125848052, "max_boundary_excess": -8.647717325013132e-07, "max_pair_overlap_depth": -3.201222129578518e-05, "metric_expression": "5.26784", "metric_symbol": "s", "metric_value": 5.267838990812585, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.2674, "setup": "peninpen", "side": 5.267838990812585, "solution_path": "data/solutions/generated/peninpen_022_07e217f200bb677e.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/07e217f200bb677e.svg", "tolerance": 1e-08, "verified": true} +{"case": "peninpen@23", "density": 0.7962909120572189, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "friedman_metric_expression": "5.34794+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.34794, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.34794+", "metric_symbol": "s", "metric_value": 5.34794, "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "1da2b8cbe37457cd", "improvement": -0.026435892305500808, "max_boundary_excess": -6.938040181393094e-06, "max_pair_overlap_depth": -1.5232433659972955e-05, "metric_expression": "5.37438", "metric_symbol": "s", "metric_value": 5.374375892305501, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.34794, "setup": "peninpen", "side": 5.374375892305501, "solution_path": "data/solutions/generated/peninpen_023_1da2b8cbe37457cd.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1da2b8cbe37457cd.svg", "tolerance": 1e-08, "verified": true} +{"case": "peninpen@24", "density": 0.7831964047098741, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "friedman_metric_expression": "5.49241+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.49241, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.49241+", "metric_symbol": "s", "metric_value": 5.49241, "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "a420bfbc7a7f6c1e", "improvement": -0.04326109388634514, "max_boundary_excess": -4.519166548492215e-06, "max_pair_overlap_depth": -1.1805376856077743e-06, "metric_expression": "5.53567", "metric_symbol": "s", "metric_value": 5.535671093886345, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.49241, "setup": "peninpen", "side": 5.535671093886345, "solution_path": "data/solutions/generated/peninpen_024_a420bfbc7a7f6c1e.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a420bfbc7a7f6c1e.svg", "tolerance": 1e-08, "verified": true} +{"case": "peninpen@25", "density": 0.7948227562651979, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "friedman_metric_expression": "5.58370+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5837, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.58370+", "metric_symbol": "s", "metric_value": 5.5837, "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "4e4dc42ba0fc7882", "improvement": -0.024646760880952634, "max_boundary_excess": -6.4042950585932436e-06, "max_pair_overlap_depth": -2.0039969058138762e-05, "metric_expression": "5.60835", "metric_symbol": "s", "metric_value": 5.608346760880953, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.5837, "setup": "peninpen", "side": 5.608346760880953, "solution_path": "data/solutions/generated/peninpen_025_4e4dc42ba0fc7882.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4e4dc42ba0fc7882.svg", "tolerance": 1e-08, "verified": true} {"case": "peninsqu@1", "density": 0.6736263863631768, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.59811, "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "metric_symbol": "s", "metric_value": 1.59811, "reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "ec216f3e37e16785", "improvement": -3.043902908794749e-05, "max_boundary_excess": -6.733207856432108e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.59814", "metric_symbol": "s", "metric_value": 1.5981404390290879, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.59811, "setup": "peninsqu", "side": 1.5981404390290879, "solution_path": "data/solutions/generated/peninsqu_001_ec216f3e37e16785.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ec216f3e37e16785.svg", "tolerance": 1e-08, "verified": true} {"case": "peninsqu@2", "density": 0.5669967061443146, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.46345+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.46345, "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "2.46345+", "metric_symbol": "s", "metric_value": 2.46345, "reference_text": "s = 2.46345+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.46345+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "bb5e10eb4917963f", "improvement": -3.0994037563569776e-05, "max_boundary_excess": -6.416866607183818e-07, "max_pair_overlap_depth": -1.473425980974552e-05, "metric_expression": "2.46348", "metric_symbol": "s", "metric_value": 2.4634809940375635, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.46345, "setup": "peninsqu", "side": 2.4634809940375635, "solution_path": "data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bb5e10eb4917963f.svg", "tolerance": 1e-08, "verified": true} {"case": "peninsqu@3", "density": 0.6102674136126431, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.90812+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.90812, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "2.90812+", "metric_symbol": "s", "metric_value": 2.90812, "reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "52b96ec8c7f6b741", "improvement": -8.50430757179943e-05, "max_boundary_excess": -3.362613813108376e-06, "max_pair_overlap_depth": -5.5799797820554886e-05, "metric_expression": "2.90821", "metric_symbol": "s", "metric_value": 2.908205043075718, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.90812, "setup": "peninsqu", "side": 2.908205043075718, "solution_path": "data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/52b96ec8c7f6b741.svg", "tolerance": 1e-08, "verified": true} @@ -338,6 +388,21 @@ {"case": "squincir@18", "density": 0.7617085472368383, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a481 / 8 = 2.741+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.741, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@18", "credit": "David W", "date": "March 2002", "family_updated": "4/13/26", "metric_expression": "\u221a481 / 8 = 2.741+", "metric_symbol": "r", "metric_value": 2.741, "reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d726e310dc0e9eaa", "improvement": -0.001627976420446764, "max_boundary_excess": -3.727763966399067e-06, "max_pair_overlap_depth": -2.573974201414142e-05, "metric_expression": "2.74263", "metric_symbol": "r", "metric_value": 2.742627976420447, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.741, "setup": "squincir", "side": 5.485255952840894, "solution_path": "data/solutions/generated/squincir_018_d726e310dc0e9eaa.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d726e310dc0e9eaa.svg", "tolerance": 1e-08, "verified": true} {"case": "squincir@19", "density": 0.7678123162790478, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.802, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "2.802+", "metric_symbol": "r", "metric_value": 2.802, "reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "b664afe5246d24cb", "improvement": -0.004559972826113423, "max_boundary_excess": -4.8887554640053565e-06, "max_pair_overlap_depth": -1.4158229616034745e-05, "metric_expression": "2.80656", "metric_symbol": "r", "metric_value": 2.8065599728261135, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.802, "setup": "squincir", "side": 5.613119945652227, "solution_path": "data/solutions/generated/squincir_019_b664afe5246d24cb.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b664afe5246d24cb.svg", "tolerance": 1e-08, "verified": true} {"case": "squincir@20", "density": 0.7585142435795145, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.893+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.893, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@20", "credit": "David W", "date": "June 2002", "family_updated": "4/13/26", "metric_expression": "2.893+", "metric_symbol": "r", "metric_value": 2.893, "reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "a6ab1017d9a75152", "improvement": -0.004064678977403258, "max_boundary_excess": -5.676979049074049e-06, "max_pair_overlap_depth": -2.975744684063919e-05, "metric_expression": "2.89706", "metric_symbol": "r", "metric_value": 2.897064678977403, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.893, "setup": "squincir", "side": 5.794129357954806, "solution_path": "data/solutions/generated/squincir_020_a6ab1017d9a75152.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a6ab1017d9a75152.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@21", "density": 0.7344962951045566, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "friedman_metric_expression": "\u221a34 / 2 = 2.915+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.915, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/13/26", "metric_expression": "\u221a34 / 2 = 2.915+", "metric_symbol": "r", "metric_value": 2.915, "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "545b9a64270c81e8", "improvement": -0.10175406268596543, "max_boundary_excess": -5.706230332691575e-06, "max_pair_overlap_depth": -2.743227626145206e-05, "metric_expression": "3.01675", "metric_symbol": "r", "metric_value": 3.0167540626859655, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.915, "setup": "squincir", "side": 6.033508125371931, "solution_path": "data/solutions/generated/squincir_021_545b9a64270c81e8.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/545b9a64270c81e8.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@22", "density": 0.7567436824354071, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "friedman_metric_expression": "3.033+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.033, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.033+", "metric_symbol": "r", "metric_value": 3.033, "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "280731f79ac45512", "improvement": -0.00901955895895279, "max_boundary_excess": -6.181418489958901e-06, "max_pair_overlap_depth": -7.085094812397941e-06, "metric_expression": "3.04202", "metric_symbol": "r", "metric_value": 3.0420195589589527, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.033, "setup": "squincir", "side": 6.084039117917905, "solution_path": "data/solutions/generated/squincir_022_280731f79ac45512.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/280731f79ac45512.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@23", "density": 0.7723110310463353, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "friedman_metric_expression": "3.073+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.073, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@23", "credit": "David W", "date": "June 2002", "family_updated": "4/13/26", "metric_expression": "3.073+", "metric_symbol": "r", "metric_value": 3.073, "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "1db15c5f1a5b8485", "improvement": -0.005880710049632754, "max_boundary_excess": -7.5142459188271005e-06, "max_pair_overlap_depth": -5.75031423715594e-06, "metric_expression": "3.07888", "metric_symbol": "r", "metric_value": 3.0788807100496327, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.073, "setup": "squincir", "side": 6.157761420099265, "solution_path": "data/solutions/generated/squincir_023_1db15c5f1a5b8485.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1db15c5f1a5b8485.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@24", "density": 0.7887737589513796, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "October 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "friedman_metric_expression": "3.110+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.11, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@24", "credit": "Maurizio Morandi", "date": "October 2010", "family_updated": "4/13/26", "metric_expression": "3.110+", "metric_symbol": "r", "metric_value": 3.11, "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "35e22c7b35c718bd", "improvement": -0.0021065491772924716, "max_boundary_excess": -5.225275177878075e-06, "max_pair_overlap_depth": -2.5024692080766187e-05, "metric_expression": "3.11211", "metric_symbol": "r", "metric_value": 3.1121065491772923, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.11, "setup": "squincir", "side": 6.224213098354585, "solution_path": "data/solutions/generated/squincir_024_35e22c7b35c718bd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/35e22c7b35c718bd.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@25", "density": 0.7754734182393866, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "April 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "friedman_metric_expression": "\u221a5809 / 24 = 3.175+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.175, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@25", "credit": "David W", "date": "April 2002", "family_updated": "4/13/26", "metric_expression": "\u221a5809 / 24 = 3.175+", "metric_symbol": "r", "metric_value": 3.175, "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "3b37ffd86fe6327a", "improvement": -0.028403237677212534, "max_boundary_excess": -6.0588717007981074e-06, "max_pair_overlap_depth": -2.0645276876063434e-05, "metric_expression": "3.20340", "metric_symbol": "r", "metric_value": 3.2034032376772124, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.175, "setup": "squincir", "side": 6.406806475354425, "solution_path": "data/solutions/generated/squincir_025_3b37ffd86fe6327a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b37ffd86fe6327a.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@26", "density": 0.7893607526867172, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "friedman_metric_expression": "\u221a41 / 2 = 3.201+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.201, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/13/26", "metric_expression": "\u221a41 / 2 = 3.201+", "metric_symbol": "r", "metric_value": 3.201, "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "b818374b7af77c7b", "improvement": -0.03697859131233283, "max_boundary_excess": -1.6484463780663816e-06, "max_pair_overlap_depth": -8.144639675689014e-06, "metric_expression": "3.23798", "metric_symbol": "r", "metric_value": 3.237978591312333, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.201, "setup": "squincir", "side": 6.475957182624666, "solution_path": "data/solutions/generated/squincir_026_b818374b7af77c7b.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b818374b7af77c7b.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@27", "density": 0.8061217783571584, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "friedman_metric_expression": "13\u221a145/48 = 3.261+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.261, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@27", "credit": "Maurizio Morandi", "date": "September 2010", "family_updated": "4/13/26", "metric_expression": "13\u221a145/48 = 3.261+", "metric_symbol": "r", "metric_value": 3.261, "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "f9fe04884031db8c", "improvement": -0.004176172420664148, "max_boundary_excess": -6.5880385129446495e-06, "max_pair_overlap_depth": -3.0313768759615556e-05, "metric_expression": "3.26518", "metric_symbol": "r", "metric_value": 3.2651761724206643, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.261, "setup": "squincir", "side": 6.5303523448413285, "solution_path": "data/solutions/generated/squincir_027_f9fe04884031db8c.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f9fe04884031db8c.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@28", "density": 0.7968013155099472, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "friedman_metric_expression": "3.333+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.333, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@28", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.333+", "metric_symbol": "r", "metric_value": 3.333, "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "011f385483141804", "improvement": -0.01148350311862334, "max_boundary_excess": -5.831944030365577e-06, "max_pair_overlap_depth": -2.2494860222238566e-05, "metric_expression": "3.34448", "metric_symbol": "r", "metric_value": 3.3444835031186235, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.333, "setup": "squincir", "side": 6.688967006237247, "solution_path": "data/solutions/generated/squincir_028_011f385483141804.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/011f385483141804.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@29", "density": 0.7843503314030067, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "friedman_metric_expression": "3.401+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.401, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@29", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.401+", "metric_symbol": "r", "metric_value": 3.401, "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "cf50b73c19c6c40b", "improvement": -0.029591604149518336, "max_boundary_excess": -4.165886964724308e-06, "max_pair_overlap_depth": -7.4185418389438595e-06, "metric_expression": "3.43059", "metric_symbol": "r", "metric_value": 3.430591604149518, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.401, "setup": "squincir", "side": 6.861183208299036, "solution_path": "data/solutions/generated/squincir_029_cf50b73c19c6c40b.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cf50b73c19c6c40b.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@30", "density": 0.7646048232029935, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "friedman_metric_expression": "3.472+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.472, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@30", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.472+", "metric_symbol": "r", "metric_value": 3.472, "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "86c752cf32b3c6a2", "improvement": -0.062005120095738775, "max_boundary_excess": -9.387146362449528e-07, "max_pair_overlap_depth": -6.215341934290297e-06, "metric_expression": "3.53401", "metric_symbol": "r", "metric_value": 3.5340051200957388, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.472, "setup": "squincir", "side": 7.0680102401914775, "solution_path": "data/solutions/generated/squincir_030_86c752cf32b3c6a2.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/86c752cf32b3c6a2.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@31", "density": 0.7887915525098625, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "friedman_metric_expression": "5 \u221a2 / 2 = 3.535+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.535, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/13/26", "metric_expression": "5 \u221a2 / 2 = 3.535+", "metric_symbol": "r", "metric_value": 3.535, "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "fdf9170d30584f4f", "improvement": -0.0019163212872146396, "max_boundary_excess": -2.62119976746078e-06, "max_pair_overlap_depth": -1.7231292489316985e-05, "metric_expression": "3.53692", "metric_symbol": "r", "metric_value": 3.536916321287215, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.535, "setup": "squincir", "side": 7.07383264257443, "solution_path": "data/solutions/generated/squincir_031_fdf9170d30584f4f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/fdf9170d30584f4f.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@32", "density": 0.7813393021086736, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "friedman_metric_expression": "3.584+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.584, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@32", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.584+", "metric_symbol": "r", "metric_value": 3.584, "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "a2628e58e58416df", "improvement": -0.026606982319385075, "max_boundary_excess": -6.923398601088593e-07, "max_pair_overlap_depth": -1.9980644787809254e-05, "metric_expression": "3.61061", "metric_symbol": "r", "metric_value": 3.610606982319385, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.584, "setup": "squincir", "side": 7.22121396463877, "solution_path": "data/solutions/generated/squincir_032_a2628e58e58416df.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a2628e58e58416df.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@33", "density": 0.7968327205597623, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@33", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "4/13/26", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "257aa24f77df5436", "improvement": -0.025767622252558464, "max_boundary_excess": -3.25349697405386e-06, "max_pair_overlap_depth": -4.400650181701771e-06, "metric_expression": "3.63077", "metric_symbol": "r", "metric_value": 3.6307676222525584, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.605, "setup": "squincir", "side": 7.261535244505117, "solution_path": "data/solutions/generated/squincir_033_257aa24f77df5436.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/257aa24f77df5436.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@34", "density": 0.8164819215284571, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_metric_expression": "3.629+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.629, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@34", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "4/13/26", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "4ba00f951e2b00e9", "improvement": -0.011753164259091342, "max_boundary_excess": -5.55479493646871e-06, "max_pair_overlap_depth": -3.971930798929435e-06, "metric_expression": "3.64075", "metric_symbol": "r", "metric_value": 3.6407531642590913, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.629, "setup": "squincir", "side": 7.281506328518183, "solution_path": "data/solutions/generated/squincir_034_4ba00f951e2b00e9.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4ba00f951e2b00e9.svg", "tolerance": 1e-08, "verified": true} +{"case": "squincir@35", "density": 0.8023678123683218, "friedman_analytical_or_proved": true, "friedman_credit": "David Eppstein", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "friedman_metric_expression": "\u221a53 / 2 = 3.640+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.64, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@35", "credit": "David Eppstein", "date": "March 2002", "family_updated": "4/13/26", "metric_expression": "\u221a53 / 2 = 3.640+", "metric_symbol": "r", "metric_value": 3.64, "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "c87a08826ad4f52f", "improvement": -0.08625298278185545, "max_boundary_excess": -2.6779267927601325e-06, "max_pair_overlap_depth": -2.0288665861567523e-05, "metric_expression": "3.72625", "metric_symbol": "r", "metric_value": 3.7262529827818556, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.64, "setup": "squincir", "side": 7.452505965563711, "solution_path": "data/solutions/generated/squincir_035_c87a08826ad4f52f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c87a08826ad4f52f.svg", "tolerance": 1e-08, "verified": true} {"case": "squindom@1", "density": 0.499990679660235, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@1", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "557f8de873a17a8e", "improvement": -9.320470070184328e-06, "max_boundary_excess": -3.7525252651882113e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000093204700702, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.0000186409401404, "solution_path": "data/solutions/generated/squindom_001_557f8de873a17a8e.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/557f8de873a17a8e.svg", "tolerance": 1e-08, "verified": true} {"case": "squindom@2", "density": 0.9999882998008334, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@2", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7684110dce2e5290", "improvement": -5.850150919473052e-06, "max_boundary_excess": -3.463373909884382e-07, "max_pair_overlap_depth": -9.41881114351023e-06, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000058501509195, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.000011700301839, "solution_path": "data/solutions/generated/squindom_002_7684110dce2e5290.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7684110dce2e5290.svg", "tolerance": 1e-08, "verified": true} {"case": "squindom@3", "density": 0.6666417193387711, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3/2 = 1.5", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@3", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "3/2 = 1.5", "metric_symbol": "s", "metric_value": 1.5, "reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3047ca63de76a853", "improvement": -2.8066531593262667e-05, "max_boundary_excess": -2.0617527398680835e-06, "max_pair_overlap_depth": -1.9554412996725112e-05, "metric_expression": "1.50003", "metric_symbol": "s", "metric_value": 1.5000280665315933, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.5, "setup": "squindom", "side": 3.0000561330631865, "solution_path": "data/solutions/generated/squindom_003_3047ca63de76a853.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3047ca63de76a853.svg", "tolerance": 1e-08, "verified": true} @@ -358,6 +423,36 @@ {"case": "squindom@18", "density": 0.9999599238999353, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@18", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a6900e1fd3f925c6", "improvement": -6.011595701327366e-05, "max_boundary_excess": -8.408701424045262e-07, "max_pair_overlap_depth": -1.079909316636929e-06, "metric_expression": "3.00006", "metric_symbol": "s", "metric_value": 3.0000601159570133, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.0001202319140265, "solution_path": "data/solutions/generated/squindom_018_a6900e1fd3f925c6.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a6900e1fd3f925c6.svg", "tolerance": 1e-08, "verified": true} {"case": "squindom@19", "density": 0.775441947176532, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3 + 1/\u221a5 = 3.447+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.447, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@19", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "8/11/12", "metric_expression": "3 + 1/\u221a5 = 3.447+", "metric_symbol": "s", "metric_value": 3.447, "reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "43609c899290294d", "improvement": -0.05315403726338541, "max_boundary_excess": -2.428479410898632e-06, "max_pair_overlap_depth": -7.462157437188033e-06, "metric_expression": "3.50015", "metric_symbol": "s", "metric_value": 3.5001540372633855, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.447, "setup": "squindom", "side": 7.000308074526771, "solution_path": "data/solutions/generated/squindom_019_43609c899290294d.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/43609c899290294d.svg", "tolerance": 1e-08, "verified": true} {"case": "squindom@20", "density": 0.8162860196976518, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@20", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4a48c58d60a1f36b", "improvement": -8.6848505622239e-05, "max_boundary_excess": -4.863306484192975e-06, "max_pair_overlap_depth": -2.3696014737728532e-05, "metric_expression": "3.50009", "metric_symbol": "s", "metric_value": 3.5000868485056222, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.0001736970112445, "solution_path": "data/solutions/generated/squindom_020_4a48c58d60a1f36b.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a48c58d60a1f36b.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@21", "density": 0.8571139620178546, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@21", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "f91a28177536f6d3", "improvement": -5.899570515355279e-05, "max_boundary_excess": -1.8534056853702905e-06, "max_pair_overlap_depth": -1.3464050134803784e-06, "metric_expression": "3.50006", "metric_symbol": "s", "metric_value": 3.5000589957051536, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.000117991410307, "solution_path": "data/solutions/generated/squindom_021_f91a28177536f6d3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f91a28177536f6d3.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@22", "density": 0.7632294028003276, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "friedman_metric_expression": "3.745+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.745, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@22", "credit": "David W", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "3.745+", "metric_symbol": "s", "metric_value": 3.745, "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "989a2d320ac47881", "improvement": -0.05137230186723096, "max_boundary_excess": -4.945995979444007e-07, "max_pair_overlap_depth": -2.0302838942054535e-05, "metric_expression": "3.79637", "metric_symbol": "s", "metric_value": 3.796372301867231, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.745, "setup": "squindom", "side": 7.592744603734462, "solution_path": "data/solutions/generated/squindom_022_989a2d320ac47881.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/989a2d320ac47881.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@23", "density": 0.7323860287330793, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "friedman_metric_expression": "3.849+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.849, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@23", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "8/11/12", "metric_expression": "3.849+", "metric_symbol": "s", "metric_value": 3.849, "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "be71e0d7682bb396", "improvement": -0.11358776902416201, "max_boundary_excess": -2.7793613528448446e-06, "max_pair_overlap_depth": -3.2193829610394076e-05, "metric_expression": "3.96259", "metric_symbol": "s", "metric_value": 3.962587769024162, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.849, "setup": "squindom", "side": 7.925175538048324, "solution_path": "data/solutions/generated/squindom_023_be71e0d7682bb396.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/be71e0d7682bb396.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@24", "density": 0.749951952861505, "friedman_analytical_or_proved": false, "friedman_credit": "DC after MM", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "friedman_metric_expression": "3.882+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.882, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@24", "credit": "DC after MM", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "3.882+", "metric_symbol": "s", "metric_value": 3.882, "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "8434a88a5e3ff85b", "improvement": -0.11812813185905613, "max_boundary_excess": -1.6922520051920742e-07, "max_pair_overlap_depth": -6.00535206030095e-06, "metric_expression": "4.00013", "metric_symbol": "s", "metric_value": 4.000128131859056, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.882, "setup": "squindom", "side": 8.000256263718112, "solution_path": "data/solutions/generated/squindom_024_8434a88a5e3ff85b.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8434a88a5e3ff85b.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@25", "density": 0.7811918228636051, "friedman_analytical_or_proved": false, "friedman_credit": "DC after MM", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "friedman_metric_expression": "3.939+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.939, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@25", "credit": "DC after MM", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "3.939+", "metric_symbol": "s", "metric_value": 3.939, "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a12363b635eb64f9", "improvement": -0.06114894178762942, "max_boundary_excess": -4.4993947669880185e-06, "max_pair_overlap_depth": -4.185053060101751e-06, "metric_expression": "4.00015", "metric_symbol": "s", "metric_value": 4.0001489417876295, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.939, "setup": "squindom", "side": 8.000297883575259, "solution_path": "data/solutions/generated/squindom_025_a12363b635eb64f9.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a12363b635eb64f9.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@26", "density": 0.8124517452057956, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "friedman_metric_expression": "3.981+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.981, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@26", "credit": "David W", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "3.981+", "metric_symbol": "s", "metric_value": 3.981, "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "e7ee6dac796acc73", "improvement": -0.019118786323000236, "max_boundary_excess": -1.3997631964635104e-06, "max_pair_overlap_depth": -1.7317256868931707e-05, "metric_expression": "4.00012", "metric_symbol": "s", "metric_value": 4.000118786323, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.981, "setup": "squindom", "side": 8.000237572646, "solution_path": "data/solutions/generated/squindom_026_e7ee6dac796acc73.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e7ee6dac796acc73.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@27", "density": 0.8436994977206457, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@27", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c68e03cc8f5005db", "improvement": -0.00011971448073744284, "max_boundary_excess": -5.175631390130775e-07, "max_pair_overlap_depth": -1.4466911184563003e-06, "metric_expression": "4.00012", "metric_symbol": "s", "metric_value": 4.000119714480737, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000239428961475, "solution_path": "data/solutions/generated/squindom_027_c68e03cc8f5005db.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c68e03cc8f5005db.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@28", "density": 0.8749068629130922, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@28", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2c8c79126d60cdac", "improvement": -0.00021290176655508475, "max_boundary_excess": -4.243746303256302e-06, "max_pair_overlap_depth": -1.6386799395987463e-05, "metric_expression": "4.00021", "metric_symbol": "s", "metric_value": 4.000212901766555, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.00042580353311, "solution_path": "data/solutions/generated/squindom_028_2c8c79126d60cdac.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2c8c79126d60cdac.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@29", "density": 0.9062096331295707, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@29", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d2548471aff7d9f5", "improvement": -8.908848335043018e-05, "max_boundary_excess": -2.8156140130519702e-06, "max_pair_overlap_depth": -2.026030487822794e-06, "metric_expression": "4.00009", "metric_symbol": "s", "metric_value": 4.00008908848335, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.0001781769667, "solution_path": "data/solutions/generated/squindom_029_d2548471aff7d9f5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d2548471aff7d9f5.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@30", "density": 0.9374597146255952, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@30", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d67a491f7b4498c0", "improvement": -8.594490193214455e-05, "max_boundary_excess": -4.188605266186585e-06, "max_pair_overlap_depth": -1.644068809536492e-06, "metric_expression": "4.00009", "metric_symbol": "s", "metric_value": 4.000085944901932, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000171889803864, "solution_path": "data/solutions/generated/squindom_030_d67a491f7b4498c0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d67a491f7b4498c0.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@31", "density": 0.7739764441627971, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@31", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0cd7148786dfe563", "improvement": -0.475092096951764, "max_boundary_excess": -3.4161928574860667e-07, "max_pair_overlap_depth": -6.1565491136228445e-06, "metric_expression": "4.47509", "metric_symbol": "s", "metric_value": 4.475092096951764, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.950184193903528, "solution_path": "data/solutions/generated/squindom_031_0cd7148786dfe563.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0cd7148786dfe563.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@32", "density": 0.7578873061721337, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@32", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "bdb0d7e9df92fbf4", "improvement": -0.5947054414830362, "max_boundary_excess": -3.94234973111196e-06, "max_pair_overlap_depth": -1.3360178682031432e-05, "metric_expression": "4.59471", "metric_symbol": "s", "metric_value": 4.594705441483036, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 9.189410882966072, "solution_path": "data/solutions/generated/squindom_032_bdb0d7e9df92fbf4.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bdb0d7e9df92fbf4.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@33", "density": 0.7924875037083852, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "friedman_metric_expression": "3 + \u221a2 = 4.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.414, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@33", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "3 + \u221a2 = 4.414+", "metric_symbol": "s", "metric_value": 4.414, "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a19cffb18f99454d", "improvement": -0.14895053406809566, "max_boundary_excess": -2.1560594953839993e-07, "max_pair_overlap_depth": -1.1686296140012153e-05, "metric_expression": "4.56295", "metric_symbol": "s", "metric_value": 4.562950534068095, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.414, "setup": "squindom", "side": 9.12590106813619, "solution_path": "data/solutions/generated/squindom_033_a19cffb18f99454d.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a19cffb18f99454d.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@34", "density": 0.7871273867322012, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "friedman_metric_expression": "4 + \u221a2/3 = 4.471+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.471, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@34", "credit": "David W", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "4 + \u221a2/3 = 4.471+", "metric_symbol": "s", "metric_value": 4.471, "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "754eaf0840f066aa", "improvement": -0.17631327368950522, "max_boundary_excess": -4.1606841634234115e-06, "max_pair_overlap_depth": -1.4162263952677279e-06, "metric_expression": "4.64731", "metric_symbol": "s", "metric_value": 4.647313273689505, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.471, "setup": "squindom", "side": 9.29462654737901, "solution_path": "data/solutions/generated/squindom_034_754eaf0840f066aa.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/754eaf0840f066aa.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@35", "density": 0.8090793490091304, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@35", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "ad3aed979d0e55b8", "improvement": -0.15075504839516718, "max_boundary_excess": -5.213118390301474e-07, "max_pair_overlap_depth": -5.817535690066933e-06, "metric_expression": "4.65076", "metric_symbol": "s", "metric_value": 4.650755048395167, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.301510096790334, "solution_path": "data/solutions/generated/squindom_035_ad3aed979d0e55b8.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ad3aed979d0e55b8.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@36", "density": 0.7686586705061, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@36", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "24e6d7b793012d54", "improvement": -0.3391544918635434, "max_boundary_excess": -1.8108160975138787e-06, "max_pair_overlap_depth": -1.3015245498015915e-05, "metric_expression": "4.83915", "metric_symbol": "s", "metric_value": 4.839154491863543, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.678308983727087, "solution_path": "data/solutions/generated/squindom_036_24e6d7b793012d54.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/24e6d7b793012d54.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@37", "density": 0.8006073518667697, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "friedman_metric_expression": "10 / 3 + \u221a2 = 4.747+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.747, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@37", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "10 / 3 + \u221a2 = 4.747+", "metric_symbol": "s", "metric_value": 4.747, "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4eb7698c43b9de17", "improvement": -0.06002164063443782, "max_boundary_excess": -4.250322036547516e-06, "max_pair_overlap_depth": -2.0290028124314574e-05, "metric_expression": "4.80702", "metric_symbol": "s", "metric_value": 4.807021640634438, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.747, "setup": "squindom", "side": 9.614043281268875, "solution_path": "data/solutions/generated/squindom_037_4eb7698c43b9de17.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4eb7698c43b9de17.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@38", "density": 0.7599740954685258, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "friedman_metric_expression": "(13 + \u221a2) / 3 = 4.804+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.804, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@38", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "(13 + \u221a2) / 3 = 4.804+", "metric_symbol": "s", "metric_value": 4.804, "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "605d8eeb30140800", "improvement": -0.19608521445298788, "max_boundary_excess": -7.686459193578797e-07, "max_pair_overlap_depth": -7.347636921672951e-06, "metric_expression": "5.00009", "metric_symbol": "s", "metric_value": 5.000085214452988, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.804, "setup": "squindom", "side": 10.000170428905976, "solution_path": "data/solutions/generated/squindom_038_605d8eeb30140800.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/605d8eeb30140800.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@39", "density": 0.8096978209200016, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "friedman_metric_expression": "4.839+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.839, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@39", "credit": "David W", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "4.839+", "metric_symbol": "s", "metric_value": 4.839, "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1909884844694062", "improvement": -0.06844928798604677, "max_boundary_excess": -1.909331257099467e-06, "max_pair_overlap_depth": -1.5029850171544012e-05, "metric_expression": "4.90745", "metric_symbol": "s", "metric_value": 4.907449287986047, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.839, "setup": "squindom", "side": 9.814898575972094, "solution_path": "data/solutions/generated/squindom_039_1909884844694062.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1909884844694062.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@40", "density": 0.812314131386038, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "friedman_metric_expression": "4.895+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.895, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@40", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "8/11/12", "metric_expression": "4.895+", "metric_symbol": "s", "metric_value": 4.895, "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c766413f09b40b68", "improvement": -0.06695696807005191, "max_boundary_excess": -4.842672254312674e-07, "max_pair_overlap_depth": -3.709534701634709e-07, "metric_expression": "4.96196", "metric_symbol": "s", "metric_value": 4.9619569680700515, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.895, "setup": "squindom", "side": 9.923913936140103, "solution_path": "data/solutions/generated/squindom_040_c766413f09b40b68.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c766413f09b40b68.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@41", "density": 0.8199463395063403, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_metric_expression": "4.927+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.927, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@41", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "8/11/12", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "41.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "41.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0c31d560a372d60c", "improvement": -0.07316360709587055, "max_boundary_excess": -3.348749109122196e-06, "max_pair_overlap_depth": -8.659590140513984e-06, "metric_expression": "5.00016", "metric_symbol": "s", "metric_value": 5.00016360709587, "n": 41, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.927, "setup": "squindom", "side": 10.00032721419174, "solution_path": "data/solutions/generated/squindom_041_0c31d560a372d60c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0c31d560a372d60c.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@42", "density": 0.8399379995423308, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "friedman_metric_expression": "4.989+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.989, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@42", "credit": "David W", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "4.989+", "metric_symbol": "s", "metric_value": 4.989, "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "source_image": "42.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "42.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "487471a1c6b8324e", "improvement": -0.011184535387124939, "max_boundary_excess": -1.9513369720058904e-06, "max_pair_overlap_depth": -9.964808349360865e-06, "metric_expression": "5.00018", "metric_symbol": "s", "metric_value": 5.000184535387125, "n": 42, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.989, "setup": "squindom", "side": 10.00036907077425, "solution_path": "data/solutions/generated/squindom_042_487471a1c6b8324e.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/487471a1c6b8324e.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@43", "density": 0.859888117316887, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@43", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7f9527ccddc9d648", "improvement": -0.00032527209571497906, "max_boundary_excess": -5.1461540806485566e-08, "max_pair_overlap_depth": -2.005039219099558e-06, "metric_expression": "5.00033", "metric_symbol": "s", "metric_value": 5.000325272095715, "n": 43, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.00065054419143, "solution_path": "data/solutions/generated/squindom_043_7f9527ccddc9d648.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7f9527ccddc9d648.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@44", "density": 0.8799631966546829, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@44", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1ffd758f1f058de5", "improvement": -0.00010455823792376862, "max_boundary_excess": -4.245467354557775e-06, "max_pair_overlap_depth": -3.962242465904708e-06, "metric_expression": "5.00010", "metric_symbol": "s", "metric_value": 5.000104558237924, "n": 44, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000209116475848, "solution_path": "data/solutions/generated/squindom_044_1ffd758f1f058de5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1ffd758f1f058de5.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@45", "density": 0.8999501217119913, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@45", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d085ed9682ca2968", "improvement": -0.00013855655918781906, "max_boundary_excess": -1.0485935568738114e-06, "max_pair_overlap_depth": -1.361329106774889e-06, "metric_expression": "5.00014", "metric_symbol": "s", "metric_value": 5.000138556559188, "n": 45, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000277113118376, "solution_path": "data/solutions/generated/squindom_045_d085ed9682ca2968.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d085ed9682ca2968.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@46", "density": 0.9198953665582859, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@46", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3b408e84cd206068", "improvement": -0.00028435426002282327, "max_boundary_excess": -1.1757865436834436e-06, "max_pair_overlap_depth": -7.423155479191479e-07, "metric_expression": "5.00028", "metric_symbol": "s", "metric_value": 5.000284354260023, "n": 46, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000568708520046, "solution_path": "data/solutions/generated/squindom_046_3b408e84cd206068.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b408e84cd206068.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@47", "density": 0.8112850662286475, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@47", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1d33d4d710718c8f", "improvement": -0.3820433347024714, "max_boundary_excess": -3.5226864758541865e-07, "max_pair_overlap_depth": -1.2150556394807666e-05, "metric_expression": "5.38204", "metric_symbol": "s", "metric_value": 5.382043334702471, "n": 47, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.764086669404943, "solution_path": "data/solutions/generated/squindom_047_1d33d4d710718c8f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1d33d4d710718c8f.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@48", "density": 0.9599518570950978, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@48", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0433c6294c4f3fe7", "improvement": -0.00012537686383318203, "max_boundary_excess": -1.0555756748686917e-06, "max_pair_overlap_depth": -4.3576353303542703e-07, "metric_expression": "5.00013", "metric_symbol": "s", "metric_value": 5.000125376863833, "n": 48, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000250753727666, "solution_path": "data/solutions/generated/squindom_048_0433c6294c4f3fe7.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0433c6294c4f3fe7.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@49", "density": 0.8116252692377275, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@49", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7b7595adf7fbed15", "improvement": -0.49421009081703016, "max_boundary_excess": -1.0264156866668372e-06, "max_pair_overlap_depth": -6.939509280323719e-06, "metric_expression": "5.49421", "metric_symbol": "s", "metric_value": 5.49421009081703, "n": 49, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.98842018163406, "solution_path": "data/solutions/generated/squindom_049_7b7595adf7fbed15.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7b7595adf7fbed15.svg", "tolerance": 1e-08, "verified": true} +{"case": "squindom@50", "density": 0.8001461788909812, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@50", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1dc2963cf23fe9ee", "improvement": -0.5896592857036387, "max_boundary_excess": -3.2315115903180924e-06, "max_pair_overlap_depth": -1.8572326916821424e-05, "metric_expression": "5.58966", "metric_symbol": "s", "metric_value": 5.589659285703639, "n": 50, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 11.179318571407277, "solution_path": "data/solutions/generated/squindom_050_1dc2963cf23fe9ee.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1dc2963cf23fe9ee.svg", "tolerance": 1e-08, "verified": true} {"case": "squinhex@1", "density": 0.6187916671304767, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a3)/6 = 0.778+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.778, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "(3+\u221a3)/6 = 0.778+", "metric_symbol": "s", "metric_value": 0.778, "reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "47260f1f9015c23d", "improvement": -0.010681817229460822, "max_boundary_excess": -3.3038085342535935e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78868", "metric_symbol": "s", "metric_value": 0.7886818172294608, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.778, "setup": "squinhex", "side": 0.7886818172294608, "solution_path": "data/solutions/generated/squinhex_001_47260f1f9015c23d.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/47260f1f9015c23d.svg", "tolerance": 1e-08, "verified": true} {"case": "squinhex@2", "density": 0.5773349997096187, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2/\u221a3 = 1.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.154, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "21fb35b9b51e59c5", "improvement": -0.0007158081621452261, "max_boundary_excess": -8.964730208767781e-07, "max_pair_overlap_depth": -4.154668371614267e-06, "metric_expression": "1.15472", "metric_symbol": "s", "metric_value": 1.1547158081621451, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.154, "setup": "squinhex", "side": 1.1547158081621451, "solution_path": "data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/21fb35b9b51e59c5.svg", "tolerance": 1e-08, "verified": true} {"case": "squinhex@3", "density": 0.6187647598988664, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(1+\u221a3)/2 = 1.366+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.366, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "(1+\u221a3)/2 = 1.366+", "metric_symbol": "s", "metric_value": 1.366, "reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a5c3dc7083e49634", "improvement": -6.667945486871218e-05, "max_boundary_excess": -1.5592677317674368e-06, "max_pair_overlap_depth": -3.548280330942233e-05, "metric_expression": "1.36607", "metric_symbol": "s", "metric_value": 1.3660666794548688, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.366, "setup": "squinhex", "side": 1.3660666794548688, "solution_path": "data/solutions/generated/squinhex_003_a5c3dc7083e49634.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a5c3dc7083e49634.svg", "tolerance": 1e-08, "verified": true} @@ -378,6 +473,26 @@ {"case": "squinhex@18", "density": 0.8107158050212577, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.92111+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.92111, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.92111+", "metric_symbol": "s", "metric_value": 2.92111, "reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "e136eeec3de765c3", "improvement": -0.0022075205933282938, "max_boundary_excess": -4.264526989622803e-06, "max_pair_overlap_depth": -7.64695502597501e-06, "metric_expression": "2.92332", "metric_symbol": "s", "metric_value": 2.9233175205933284, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.92111, "setup": "squinhex", "side": 2.9233175205933284, "solution_path": "data/solutions/generated/squinhex_018_e136eeec3de765c3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e136eeec3de765c3.svg", "tolerance": 1e-08, "verified": true} {"case": "squinhex@19", "density": 0.8472470384096148, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.93511+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.93511, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.93511+", "metric_symbol": "s", "metric_value": 2.93511, "reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "ae3850bdb0ac1880", "improvement": -0.0028496545666087947, "max_boundary_excess": -6.965076151420116e-06, "max_pair_overlap_depth": -7.201359447650546e-06, "metric_expression": "2.93796", "metric_symbol": "s", "metric_value": 2.9379596545666087, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.93511, "setup": "squinhex", "side": 2.9379596545666087, "solution_path": "data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ae3850bdb0ac1880.svg", "tolerance": 1e-08, "verified": true} {"case": "squinhex@20", "density": 0.7671837266988989, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.16123+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.16123, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.16123+", "metric_symbol": "s", "metric_value": 3.16123, "reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "6b12994046713635", "improvement": -0.0064358571960680955, "max_boundary_excess": -2.567971421646714e-06, "max_pair_overlap_depth": -2.07090961877876e-05, "metric_expression": "3.16767", "metric_symbol": "s", "metric_value": 3.1676658571960683, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.16123, "setup": "squinhex", "side": 3.1676658571960683, "solution_path": "data/solutions/generated/squinhex_020_6b12994046713635.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6b12994046713635.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@21", "density": 0.7670273555344158, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_metric_expression": "3.23496+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.23496, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3a812c823f86feb7", "improvement": -0.011262455551525274, "max_boundary_excess": -1.638368640602293e-06, "max_pair_overlap_depth": -6.590999670152975e-06, "metric_expression": "3.24622", "metric_symbol": "s", "metric_value": 3.2462224555515253, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.23496, "setup": "squinhex", "side": 3.2462224555515253, "solution_path": "data/solutions/generated/squinhex_021_3a812c823f86feb7.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3a812c823f86feb7.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@22", "density": 0.770525380181529, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "friedman_metric_expression": "3.31573+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.31573, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.31573+", "metric_symbol": "s", "metric_value": 3.31573, "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a1e7eaf12003fa2e", "improvement": 0.0006659560348909466, "max_boundary_excess": -2.169977234601665e-06, "max_pair_overlap_depth": -1.9814540655582746e-05, "metric_expression": "3.31506", "metric_symbol": "s", "metric_value": 3.315064043965109, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.31573, "setup": "squinhex", "side": 3.315064043965109, "solution_path": "data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a1e7eaf12003fa2e.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@23", "density": 0.7678817589014695, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "friedman_metric_expression": "3.36437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.36437, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.36437+", "metric_symbol": "s", "metric_value": 3.36437, "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "c418f25bcf52655a", "improvement": -0.031028866190116577, "max_boundary_excess": -3.0072288037779673e-06, "max_pair_overlap_depth": -3.3623152545181334e-05, "metric_expression": "3.39540", "metric_symbol": "s", "metric_value": 3.3953988661901167, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.36437, "setup": "squinhex", "side": 3.3953988661901167, "solution_path": "data/solutions/generated/squinhex_023_c418f25bcf52655a.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c418f25bcf52655a.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@24", "density": 0.7853118981105532, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "friedman_metric_expression": "3.41524+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.41524, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.41524+", "metric_symbol": "s", "metric_value": 3.41524, "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "94da47c0085910e3", "improvement": -0.014479391564234945, "max_boundary_excess": -2.620667464817998e-06, "max_pair_overlap_depth": -1.0754243918387196e-05, "metric_expression": "3.42972", "metric_symbol": "s", "metric_value": 3.4297193915642348, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.41524, "setup": "squinhex", "side": 3.4297193915642348, "solution_path": "data/solutions/generated/squinhex_024_94da47c0085910e3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/94da47c0085910e3.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@25", "density": 0.7979870877832509, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "friedman_metric_expression": "2\u221a3 = 3.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4641, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@25", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2\u221a3 = 3.46410+", "metric_symbol": "s", "metric_value": 3.4641, "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "e42cc21b7cb42f7c", "improvement": -0.008430980948480382, "max_boundary_excess": -4.683096739436409e-06, "max_pair_overlap_depth": -1.8538188668593136e-06, "metric_expression": "3.47253", "metric_symbol": "s", "metric_value": 3.4725309809484806, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.4641, "setup": "squinhex", "side": 3.4725309809484806, "solution_path": "data/solutions/generated/squinhex_025_e42cc21b7cb42f7c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e42cc21b7cb42f7c.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@26", "density": 0.8081929307719398, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "friedman_metric_expression": "3.4939927+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4939927, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.4939927+", "metric_symbol": "s", "metric_value": 3.4939927, "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "source_image": "26.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "ffb43ba6e2cd5818", "improvement": -0.02487717357936603, "max_boundary_excess": -9.15748884603073e-07, "max_pair_overlap_depth": -3.1303960409623244e-05, "metric_expression": "3.51887", "metric_symbol": "s", "metric_value": 3.518869873579366, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.4939927, "setup": "squinhex", "side": 3.518869873579366, "solution_path": "data/solutions/generated/squinhex_026_ffb43ba6e2cd5818.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ffb43ba6e2cd5818.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@27", "density": 0.8212390180142829, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "friedman_metric_expression": "(9+7\u221a3)/6 = 3.52072+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.52072, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@27", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "(9+7\u221a3)/6 = 3.52072+", "metric_symbol": "s", "metric_value": 3.52072, "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "source_image": "27.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "27.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1daf4383b04cfd35", "improvement": -0.03658539789192261, "max_boundary_excess": -5.73679317656282e-06, "max_pair_overlap_depth": -8.244431831005983e-06, "metric_expression": "3.55731", "metric_symbol": "s", "metric_value": 3.5573053978919225, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.52072, "setup": "squinhex", "side": 3.5573053978919225, "solution_path": "data/solutions/generated/squinhex_027_1daf4383b04cfd35.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1daf4383b04cfd35.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@28", "density": 0.8148431181294798, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "friedman_metric_expression": "3.62565+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.62565, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.62565+", "metric_symbol": "s", "metric_value": 3.62565, "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "source_image": "28.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a261c762e391859b", "improvement": -0.011121972861151797, "max_boundary_excess": -1.2588144775567533e-07, "max_pair_overlap_depth": -1.6737569052738266e-05, "metric_expression": "3.63677", "metric_symbol": "s", "metric_value": 3.6367719728611516, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.62565, "setup": "squinhex", "side": 3.6367719728611516, "solution_path": "data/solutions/generated/squinhex_028_a261c762e391859b.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a261c762e391859b.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@29", "density": 0.8153965094821096, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "friedman_metric_expression": "3.66437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.66437, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@29", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.66437+", "metric_symbol": "s", "metric_value": 3.66437, "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "source_image": "29.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "29.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b4f34cc71652a9b5", "improvement": -0.03551846072849152, "max_boundary_excess": -4.2642198528972326e-06, "max_pair_overlap_depth": -2.258360826079553e-05, "metric_expression": "3.69989", "metric_symbol": "s", "metric_value": 3.6998884607284914, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.66437, "setup": "squinhex", "side": 3.6998884607284914, "solution_path": "data/solutions/generated/squinhex_029_b4f34cc71652a9b5.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4f34cc71652a9b5.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@30", "density": 0.837162051280775, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "friedman_metric_expression": "3.69554+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.69554, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.69554+", "metric_symbol": "s", "metric_value": 3.69554, "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "source_image": "30.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "30.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "622f4b213176ff50", "improvement": -0.01835753389360395, "max_boundary_excess": -4.942525026869045e-06, "max_pair_overlap_depth": -2.8250288841569215e-05, "metric_expression": "3.71390", "metric_symbol": "s", "metric_value": 3.7138975338936038, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.69554, "setup": "squinhex", "side": 3.7138975338936038, "solution_path": "data/solutions/generated/squinhex_030_622f4b213176ff50.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/622f4b213176ff50.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@31", "density": 0.8285110718813824, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "friedman_metric_expression": "3.78410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7841, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.78410+", "metric_symbol": "s", "metric_value": 3.7841, "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "5ef6ed65925f4bf8", "improvement": -0.010847266536003097, "max_boundary_excess": -1.2328982304959355e-06, "max_pair_overlap_depth": -1.5474800372561326e-05, "metric_expression": "3.79495", "metric_symbol": "s", "metric_value": 3.794947266536003, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.7841, "setup": "squinhex", "side": 3.794947266536003, "solution_path": "data/solutions/generated/squinhex_031_5ef6ed65925f4bf8.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5ef6ed65925f4bf8.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@32", "density": 0.8139313062277866, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "friedman_metric_expression": "3.84795+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.84795, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.84795+", "metric_symbol": "s", "metric_value": 3.84795, "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3fefe3c7860a7042", "improvement": -0.04209987405059623, "max_boundary_excess": -9.31294317671141e-06, "max_pair_overlap_depth": -5.122637159571397e-06, "metric_expression": "3.89005", "metric_symbol": "s", "metric_value": 3.890049874050596, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.84795, "setup": "squinhex", "side": 3.890049874050596, "solution_path": "data/solutions/generated/squinhex_032_3fefe3c7860a7042.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3fefe3c7860a7042.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@33", "density": 0.8232428856624427, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "friedman_metric_expression": "3.88897+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.88897, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.88897+", "metric_symbol": "s", "metric_value": 3.88897, "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "75f6c6042636af47", "improvement": -0.038989792359782616, "max_boundary_excess": -8.523200217199587e-07, "max_pair_overlap_depth": -1.020864303750979e-05, "metric_expression": "3.92796", "metric_symbol": "s", "metric_value": 3.9279597923597827, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.88897, "setup": "squinhex", "side": 3.9279597923597827, "solution_path": "data/solutions/generated/squinhex_033_75f6c6042636af47.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/75f6c6042636af47.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@34", "density": 0.8011598710060369, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "friedman_metric_expression": "3.92704+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.92704, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.92704+", "metric_symbol": "s", "metric_value": 3.92704, "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "9936488a40de24d9", "improvement": -0.11456551352210997, "max_boundary_excess": -4.6100121240738093e-07, "max_pair_overlap_depth": -4.74894416568894e-06, "metric_expression": "4.04161", "metric_symbol": "s", "metric_value": 4.04160551352211, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.92704, "setup": "squinhex", "side": 4.04160551352211, "solution_path": "data/solutions/generated/squinhex_034_9936488a40de24d9.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9936488a40de24d9.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@35", "density": 0.8247475431755152, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "friedman_metric_expression": "3.99833+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.99833, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.99833+", "metric_symbol": "s", "metric_value": 3.99833, "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "af16853a8ef97483", "improvement": -0.04321634902297422, "max_boundary_excess": -2.7980290841403613e-07, "max_pair_overlap_depth": -1.2096346981849138e-06, "metric_expression": "4.04155", "metric_symbol": "s", "metric_value": 4.041546349022974, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.99833, "setup": "squinhex", "side": 4.041546349022974, "solution_path": "data/solutions/generated/squinhex_035_af16853a8ef97483.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/af16853a8ef97483.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@36", "density": 0.8483249224466834, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_metric_expression": "4.03258+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.03258, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.03258+", "metric_symbol": "s", "metric_value": 4.03258, "reference_text": "s = 4.03258+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.03258+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a763846075248773", "improvement": -0.008934991863539743, "max_boundary_excess": -2.1813389232689927e-06, "max_pair_overlap_depth": -6.121205389897355e-06, "metric_expression": "4.04151", "metric_symbol": "s", "metric_value": 4.04151499186354, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.03258, "setup": "squinhex", "side": 4.04151499186354, "solution_path": "data/solutions/generated/squinhex_036_a763846075248773.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a763846075248773.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@37", "density": 0.8718839158050435, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "friedman_metric_expression": "7/\u221a3 = 4.04145+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.04145, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@37", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "7/\u221a3 = 4.04145+", "metric_symbol": "s", "metric_value": 4.04145, "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "source_image": "37.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "friedman_source_image": "37.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a455ecb05be301ad", "improvement": -7.79426845127773e-05, "max_boundary_excess": -1.1637259667017477e-06, "max_pair_overlap_depth": -1.0162747484221413e-05, "metric_expression": "4.04153", "metric_symbol": "s", "metric_value": 4.041527942684513, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.04145, "setup": "squinhex", "side": 4.041527942684513, "solution_path": "data/solutions/generated/squinhex_037_a455ecb05be301ad.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a455ecb05be301ad.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@38", "density": 0.8350388271501855, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "friedman_metric_expression": "4.18476+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.18476, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.18476+", "metric_symbol": "s", "metric_value": 4.18476, "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "bcbfc88586b3e923", "improvement": -0.00040437963386885656, "max_boundary_excess": -1.1747860476968907e-06, "max_pair_overlap_depth": -1.7875980621084864e-05, "metric_expression": "4.18516", "metric_symbol": "s", "metric_value": 4.185164379633869, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.18476, "setup": "squinhex", "side": 4.185164379633869, "solution_path": "data/solutions/generated/squinhex_038_bcbfc88586b3e923.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bcbfc88586b3e923.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@39", "density": 0.8275155837189719, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "friedman_metric_expression": "4.25744+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.25744, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.25744+", "metric_symbol": "s", "metric_value": 4.25744, "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "85e7e9eb3b3b7f5f", "improvement": -0.001664243334674076, "max_boundary_excess": -3.204496689819836e-06, "max_pair_overlap_depth": -1.602842749781619e-05, "metric_expression": "4.25910", "metric_symbol": "s", "metric_value": 4.259104243334674, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.25744, "setup": "squinhex", "side": 4.259104243334674, "solution_path": "data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/85e7e9eb3b3b7f5f.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinhex@40", "density": 0.8287778526415311, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "friedman_metric_expression": "4.31157+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.31157, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.31157+", "metric_symbol": "s", "metric_value": 4.31157, "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "f7dadd815b6542ca", "improvement": 0.00149344623519454, "max_boundary_excess": -3.946410988960316e-06, "max_pair_overlap_depth": -1.2739218361978999e-05, "metric_expression": "4.31008", "metric_symbol": "s", "metric_value": 4.310076553764805, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.31157, "setup": "squinhex", "side": 4.310076553764805, "solution_path": "data/solutions/generated/squinhex_040_f7dadd815b6542ca.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f7dadd815b6542ca.svg", "tolerance": 1e-08, "verified": true} {"case": "squinoct@1", "density": 0.7071036297921394, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1/\u221a(2+\u221a2) = .54119+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.54119, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@1", "credit": "Trivial", "date": "", "family_updated": "3/17/26", "metric_expression": "1/\u221a(2+\u221a2) = .54119+", "metric_symbol": "s", "metric_value": 0.54119, "reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "b63c90f60717ba08", "improvement": -7.30613665711477e-06, "max_boundary_excess": -1.1705346114441018e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.54120", "metric_symbol": "s", "metric_value": 0.5411973061366571, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.54119, "setup": "squinoct", "side": 0.5411973061366571, "solution_path": "data/solutions/generated/squinoct_001_b63c90f60717ba08.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b63c90f60717ba08.svg", "tolerance": 1e-08, "verified": true} {"case": "squinoct@2", "density": 0.5389047922692529, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": ".87667+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.87667, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@2", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "3/17/26", "metric_expression": ".87667+", "metric_symbol": "s", "metric_value": 0.87667, "reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7194ac58cba12fa7", "improvement": -4.0351762315649076e-05, "max_boundary_excess": -8.607981571160174e-06, "max_pair_overlap_depth": -1.1896285956325414e-06, "metric_expression": "0.87671", "metric_symbol": "s", "metric_value": 0.8767103517623156, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.87667, "setup": "squinoct", "side": 0.8767103517623156, "solution_path": "data/solutions/generated/squinoct_002_7194ac58cba12fa7.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7194ac58cba12fa7.svg", "tolerance": 1e-08, "verified": true} {"case": "squinoct@3", "density": 0.5862650280603752, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0294, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@3", "credit": "Erich Friedman", "date": "December 2013", "family_updated": "3/17/26", "metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "metric_symbol": "s", "metric_value": 1.0294, "reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3d85991afac60053", "improvement": -6.311956912941064e-05, "max_boundary_excess": -1.835100684478856e-06, "max_pair_overlap_depth": -3.4409461626638826e-05, "metric_expression": "1.02946", "metric_symbol": "s", "metric_value": 1.0294631195691295, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0294, "setup": "squinoct", "side": 1.0294631195691295, "solution_path": "data/solutions/generated/squinoct_003_3d85991afac60053.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3d85991afac60053.svg", "tolerance": 1e-08, "verified": true} @@ -398,6 +513,16 @@ {"case": "squinoct@18", "density": 0.7934296897658486, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.16778+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.16778, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.16778+", "metric_symbol": "s", "metric_value": 2.16778, "reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a7275e2ab7024187", "improvement": 0.00017977070139485463, "max_boundary_excess": -2.9711774532196686e-06, "max_pair_overlap_depth": -1.4522556675777842e-05, "metric_expression": "2.16760", "metric_symbol": "s", "metric_value": 2.167600229298605, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.16778, "setup": "squinoct", "side": 2.167600229298605, "solution_path": "data/solutions/generated/squinoct_018_a7275e2ab7024187.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a7275e2ab7024187.svg", "tolerance": 1e-08, "verified": true} {"case": "squinoct@19", "density": 0.793469906795261, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.22823+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.22823, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.22823+", "metric_symbol": "s", "metric_value": 2.22823, "reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "330906f1db929cdb", "improvement": 0.0012889040224068893, "max_boundary_excess": -1.0543459428412958e-06, "max_pair_overlap_depth": -1.4850274468458657e-05, "metric_expression": "2.22694", "metric_symbol": "s", "metric_value": 2.226941095977593, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.22823, "setup": "squinoct", "side": 2.226941095977593, "solution_path": "data/solutions/generated/squinoct_019_330906f1db929cdb.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/330906f1db929cdb.svg", "tolerance": 1e-08, "verified": true} {"case": "squinoct@20", "density": 0.7898975362386181, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.28730+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.2873, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.28730+", "metric_symbol": "s", "metric_value": 2.2873, "reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a51f6ff7158a3148", "improvement": -0.0026541016910699433, "max_boundary_excess": -1.638361599013347e-06, "max_pair_overlap_depth": -2.1188903268742898e-05, "metric_expression": "2.28995", "metric_symbol": "s", "metric_value": 2.28995410169107, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.2873, "setup": "squinoct", "side": 2.28995410169107, "solution_path": "data/solutions/generated/squinoct_020_a51f6ff7158a3148.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a51f6ff7158a3148.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@21", "density": 0.8091484006744551, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "friedman_metric_expression": "2.32167+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32167, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.32167+", "metric_symbol": "s", "metric_value": 2.32167, "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a3759fa0325bb184", "improvement": 0.0032467851108277657, "max_boundary_excess": -2.288437924896875e-06, "max_pair_overlap_depth": -7.589979277911052e-06, "metric_expression": "2.31842", "metric_symbol": "s", "metric_value": 2.3184232148891724, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.32167, "setup": "squinoct", "side": 2.3184232148891724, "solution_path": "data/solutions/generated/squinoct_021_a3759fa0325bb184.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a3759fa0325bb184.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@22", "density": 0.7774325610742356, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "friedman_metric_expression": "2.41811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.41811, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.41811+", "metric_symbol": "s", "metric_value": 2.41811, "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "bebb10254b247f18", "improvement": -0.0027915964915901093, "max_boundary_excess": -1.6967368563790073e-06, "max_pair_overlap_depth": -1.7892080061754356e-05, "metric_expression": "2.42090", "metric_symbol": "s", "metric_value": 2.42090159649159, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.41811, "setup": "squinoct", "side": 2.42090159649159, "solution_path": "data/solutions/generated/squinoct_022_bebb10254b247f18.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bebb10254b247f18.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@23", "density": 0.7777209980912639, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "friedman_metric_expression": "2.47329+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.47329, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.47329+", "metric_symbol": "s", "metric_value": 2.47329, "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "004d1c5d4d7bca47", "improvement": -0.0015616154620987643, "max_boundary_excess": -4.985478608046375e-06, "max_pair_overlap_depth": -1.4996046389881279e-05, "metric_expression": "2.47485", "metric_symbol": "s", "metric_value": 2.4748516154620988, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.47329, "setup": "squinoct", "side": 2.4748516154620988, "solution_path": "data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/004d1c5d4d7bca47.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@24", "density": 0.804709078453695, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "friedman_metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.48528, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@24", "credit": "Trivial", "date": "", "family_updated": "3/17/26", "metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "metric_symbol": "s", "metric_value": 2.48528, "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "4f255616aca5e547", "improvement": -4.580955124477981e-05, "max_boundary_excess": -4.67146332394231e-06, "max_pair_overlap_depth": -9.95881463161652e-06, "metric_expression": "2.48533", "metric_symbol": "s", "metric_value": 2.4853258095512447, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.48528, "setup": "squinoct", "side": 2.4853258095512447, "solution_path": "data/solutions/generated/squinoct_024_4f255616aca5e547.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4f255616aca5e547.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@25", "density": 0.8181498541161091, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "friedman_metric_expression": "11/(3+\u221a2) = 2.49195+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.49195, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "11/(3+\u221a2) = 2.49195+", "metric_symbol": "s", "metric_value": 2.49195, "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "cf47f0214a5dc773", "improvement": -0.023702995861961007, "max_boundary_excess": -3.2684625650520232e-06, "max_pair_overlap_depth": -1.853051245270798e-05, "metric_expression": "2.51565", "metric_symbol": "s", "metric_value": 2.515652995861961, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.49195, "setup": "squinoct", "side": 2.515652995861961, "solution_path": "data/solutions/generated/squinoct_025_cf47f0214a5dc773.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cf47f0214a5dc773.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@26", "density": 0.8074475115340339, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "friedman_metric_expression": "2.52841+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.52841, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.52841+", "metric_symbol": "s", "metric_value": 2.52841, "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "5b23f9a6c0d60139", "improvement": -0.054008850877670156, "max_boundary_excess": -2.200162939176049e-06, "max_pair_overlap_depth": -3.6095353424636656e-05, "metric_expression": "2.58242", "metric_symbol": "s", "metric_value": 2.58241885087767, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.52841, "setup": "squinoct", "side": 2.58241885087767, "solution_path": "data/solutions/generated/squinoct_026_5b23f9a6c0d60139.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5b23f9a6c0d60139.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@27", "density": 0.8082183491889691, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "friedman_metric_expression": "2.58695+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.58695, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.58695+", "metric_symbol": "s", "metric_value": 2.58695, "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7199a9fabf8295f3", "improvement": -0.0434069531833039, "max_boundary_excess": -5.468946855752342e-06, "max_pair_overlap_depth": -2.0325723741110302e-05, "metric_expression": "2.63036", "metric_symbol": "s", "metric_value": 2.6303569531833038, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.58695, "setup": "squinoct", "side": 2.6303569531833038, "solution_path": "data/solutions/generated/squinoct_027_7199a9fabf8295f3.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7199a9fabf8295f3.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@28", "density": 0.8358880435909333, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "friedman_metric_expression": "2.63116+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.63116, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.63116+", "metric_symbol": "s", "metric_value": 2.63116, "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "ad6175b5666f3771", "improvement": -0.002757201469966386, "max_boundary_excess": -5.321806274664218e-06, "max_pair_overlap_depth": -2.3625714268504794e-05, "metric_expression": "2.63392", "metric_symbol": "s", "metric_value": 2.6339172014699663, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.63116, "setup": "squinoct", "side": 2.6339172014699663, "solution_path": "data/solutions/generated/squinoct_028_ad6175b5666f3771.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ad6175b5666f3771.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@29", "density": 0.8053277894510656, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "friedman_metric_expression": "2.70811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.70811, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.70811+", "metric_symbol": "s", "metric_value": 2.70811, "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a7c60552360644b6", "improvement": -0.02281526721143523, "max_boundary_excess": -3.928573599716161e-06, "max_pair_overlap_depth": -2.4601383313171965e-05, "metric_expression": "2.73093", "metric_symbol": "s", "metric_value": 2.7309252672114352, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.70811, "setup": "squinoct", "side": 2.7309252672114352, "solution_path": "data/solutions/generated/squinoct_029_a7c60552360644b6.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a7c60552360644b6.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinoct@30", "density": 0.8050487180673215, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "friedman_metric_expression": "2.74220+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.7422, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.74220+", "metric_symbol": "s", "metric_value": 2.7422, "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "8d25a2ea5990135c", "improvement": -0.03589252210129912, "max_boundary_excess": -4.415473577555007e-06, "max_pair_overlap_depth": -7.985805165922066e-06, "metric_expression": "2.77809", "metric_symbol": "s", "metric_value": 2.778092522101299, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.7422, "setup": "squinoct", "side": 2.778092522101299, "solution_path": "data/solutions/generated/squinoct_030_8d25a2ea5990135c.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8d25a2ea5990135c.svg", "tolerance": 1e-08, "verified": true} {"case": "squinpen@1", "density": 0.6621920830904189, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": ".936+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.936, "friedman_reference": {"analytical_or_proved": true, "case": "squinpen@1", "credit": "Trivial", "date": "", "family_updated": "4/8/26", "metric_expression": ".936+", "metric_symbol": "s", "metric_value": 0.936, "reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7c4deaf46828e45f", "improvement": -0.0008790374068264883, "max_boundary_excess": -1.1116494686738636e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.93688", "metric_symbol": "s", "metric_value": 0.9368790374068265, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.936, "setup": "squinpen", "side": 0.9368790374068265, "solution_path": "data/solutions/generated/squinpen_001_7c4deaf46828e45f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7c4deaf46828e45f.svg", "tolerance": 1e-08, "verified": true} {"case": "squinpen@2", "density": 0.49287502021209156, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.535+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.535, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@2", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "4/8/26", "metric_expression": "1.535+", "metric_symbol": "s", "metric_value": 1.535, "reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "e0d70422bfa035f2", "improvement": -0.0007556004426736429, "max_boundary_excess": -5.603512178169518e-07, "max_pair_overlap_depth": -4.1992473865937185e-06, "metric_expression": "1.53576", "metric_symbol": "s", "metric_value": 1.5357556004426736, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.535, "setup": "squinpen", "side": 1.5357556004426736, "solution_path": "data/solutions/generated/squinpen_002_e0d70422bfa035f2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e0d70422bfa035f2.svg", "tolerance": 1e-08, "verified": true} {"case": "squinpen@3", "density": 0.6064545372240481, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.695+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.695, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@3", "credit": "David W", "date": "July 2012", "family_updated": "4/8/26", "metric_expression": "1.695+", "metric_symbol": "s", "metric_value": 1.695, "reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "20345bd1acea07ee", "improvement": -0.0006531320538840646, "max_boundary_excess": -5.096669049020619e-07, "max_pair_overlap_depth": -2.3507012493845236e-05, "metric_expression": "1.69565", "metric_symbol": "s", "metric_value": 1.6956531320538841, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.695, "setup": "squinpen", "side": 1.6956531320538841, "solution_path": "data/solutions/generated/squinpen_003_20345bd1acea07ee.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/20345bd1acea07ee.svg", "tolerance": 1e-08, "verified": true} @@ -418,7 +543,26 @@ {"case": "squinpen@18", "density": 0.7949963635829483, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.626+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.626, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/8/26", "metric_expression": "3.626+", "metric_symbol": "s", "metric_value": 3.626, "reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "521e6ed1020d53e6", "improvement": -0.001681876520355896, "max_boundary_excess": -2.132718950610418e-06, "max_pair_overlap_depth": -5.952134619235938e-06, "metric_expression": "3.62768", "metric_symbol": "s", "metric_value": 3.627681876520356, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.626, "setup": "squinpen", "side": 3.627681876520356, "solution_path": "data/solutions/generated/squinpen_018_521e6ed1020d53e6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/521e6ed1020d53e6.svg", "tolerance": 1e-08, "verified": true} {"case": "squinpen@19", "density": 0.8016091392666894, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.710+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.71, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/8/26", "metric_expression": "3.710+", "metric_symbol": "s", "metric_value": 3.71, "reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "66aeca1af6b9bf65", "improvement": -0.001683910599032501, "max_boundary_excess": -5.240508232322902e-06, "max_pair_overlap_depth": -2.033383687716217e-05, "metric_expression": "3.71168", "metric_symbol": "s", "metric_value": 3.7116839105990325, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.71, "setup": "squinpen", "side": 3.7116839105990325, "solution_path": "data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/66aeca1af6b9bf65.svg", "tolerance": 1e-08, "verified": true} {"case": "squinpen@20", "density": 0.8030009751844291, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.802+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.802, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/8/26", "metric_expression": "3.802+", "metric_symbol": "s", "metric_value": 3.802, "reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "8424f972564f51a8", "improvement": -0.00280562795003636, "max_boundary_excess": -2.488842199203112e-06, "max_pair_overlap_depth": -3.2279665458823104e-05, "metric_expression": "3.80481", "metric_symbol": "s", "metric_value": 3.8048056279500364, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.802, "setup": "squinpen", "side": 3.8048056279500364, "solution_path": "data/solutions/generated/squinpen_020_8424f972564f51a8.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8424f972564f51a8.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@21", "density": 0.8135799833496993, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "friedman_metric_expression": "3.864+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.864, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "3.864+", "metric_symbol": "s", "metric_value": 3.864, "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "3fc16f4ddfd45967", "improvement": -0.009334763632923071, "max_boundary_excess": -5.959133691049833e-07, "max_pair_overlap_depth": -1.419469897068204e-05, "metric_expression": "3.87333", "metric_symbol": "s", "metric_value": 3.873334763632923, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.864, "setup": "squinpen", "side": 3.873334763632923, "solution_path": "data/solutions/generated/squinpen_021_3fc16f4ddfd45967.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3fc16f4ddfd45967.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@22", "density": 0.8236901899623935, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "friedman_metric_expression": "3.937+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.937, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "3.937+", "metric_symbol": "s", "metric_value": 3.937, "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "33b95c59890c6cd7", "improvement": -0.0030787983666398233, "max_boundary_excess": -3.1912141987053604e-06, "max_pair_overlap_depth": -2.2837560550437175e-06, "metric_expression": "3.94008", "metric_symbol": "s", "metric_value": 3.9400787983666397, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.937, "setup": "squinpen", "side": 3.9400787983666397, "solution_path": "data/solutions/generated/squinpen_022_33b95c59890c6cd7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/33b95c59890c6cd7.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@23", "density": 0.8342850114016098, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "friedman_metric_expression": "4.002+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.002, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.002+", "metric_symbol": "s", "metric_value": 4.002, "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "125d15e1f42d4cc7", "improvement": -0.000968856434470311, "max_boundary_excess": -3.142206802972531e-06, "max_pair_overlap_depth": -1.3381668518996914e-05, "metric_expression": "4.00297", "metric_symbol": "s", "metric_value": 4.00296885643447, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.002, "setup": "squinpen", "side": 4.00296885643447, "solution_path": "data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/125d15e1f42d4cc7.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@24", "density": 0.8138659237502952, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "friedman_metric_expression": "4.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.107, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.107+", "metric_symbol": "s", "metric_value": 4.107, "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "5483079483431bd6", "improvement": -0.03304157256133866, "max_boundary_excess": -1.9102638477275247e-07, "max_pair_overlap_depth": -2.2611945261152844e-05, "metric_expression": "4.14004", "metric_symbol": "s", "metric_value": 4.140041572561339, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.107, "setup": "squinpen", "side": 4.140041572561339, "solution_path": "data/solutions/generated/squinpen_024_5483079483431bd6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5483079483431bd6.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@25", "density": 0.8346264431391957, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "friedman_metric_expression": "4.169+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.169, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.169+", "metric_symbol": "s", "metric_value": 4.169, "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "965f543dd3a1a5b2", "improvement": -0.003529809873594303, "max_boundary_excess": -4.8760801669609005e-06, "max_pair_overlap_depth": -9.22783607931743e-06, "metric_expression": "4.17253", "metric_symbol": "s", "metric_value": 4.172529809873594, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.169, "setup": "squinpen", "side": 4.172529809873594, "solution_path": "data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/965f543dd3a1a5b2.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@26", "density": 0.846720772454187, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "friedman_metric_expression": "4.223+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.223, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@26", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.223+", "metric_symbol": "s", "metric_value": 4.223, "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "12ea954c92ca25d9", "improvement": -0.0016630925283189768, "max_boundary_excess": -5.329734777233707e-07, "max_pair_overlap_depth": -5.080948892621784e-06, "metric_expression": "4.22466", "metric_symbol": "s", "metric_value": 4.224663092528319, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.223, "setup": "squinpen", "side": 4.224663092528319, "solution_path": "data/solutions/generated/squinpen_026_12ea954c92ca25d9.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/12ea954c92ca25d9.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@27", "density": 0.8216861987406389, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "friedman_metric_expression": "4.350+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.35, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@27", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.350+", "metric_symbol": "s", "metric_value": 4.35, "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c69ed1bfb373f6cd", "improvement": -0.020231063660665072, "max_boundary_excess": -1.6360588600815792e-06, "max_pair_overlap_depth": -1.2793416169033789e-05, "metric_expression": "4.37023", "metric_symbol": "s", "metric_value": 4.370231063660665, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.35, "setup": "squinpen", "side": 4.370231063660665, "solution_path": "data/solutions/generated/squinpen_027_c69ed1bfb373f6cd.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c69ed1bfb373f6cd.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@28", "density": 0.8217452867794004, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "friedman_metric_expression": "4.421+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.421, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@28", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.421+", "metric_symbol": "s", "metric_value": 4.421, "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "117dfd2e5e6c3a3f", "improvement": -0.02926547059333995, "max_boundary_excess": -1.5377994807666766e-06, "max_pair_overlap_depth": -1.4777589123937673e-05, "metric_expression": "4.45027", "metric_symbol": "s", "metric_value": 4.45026547059334, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.421, "setup": "squinpen", "side": 4.45026547059334, "solution_path": "data/solutions/generated/squinpen_028_117dfd2e5e6c3a3f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/117dfd2e5e6c3a3f.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@29", "density": 0.8184635083200854, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "friedman_metric_expression": "4.499+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.499, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.499+", "metric_symbol": "s", "metric_value": 4.499, "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c1c4dc57f8cd7d32", "improvement": -0.03910826264420031, "max_boundary_excess": -4.357708770048677e-06, "max_pair_overlap_depth": -3.1603738400165504e-05, "metric_expression": "4.53811", "metric_symbol": "s", "metric_value": 4.5381082626442, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.499, "setup": "squinpen", "side": 4.5381082626442, "solution_path": "data/solutions/generated/squinpen_029_c1c4dc57f8cd7d32.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c1c4dc57f8cd7d32.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@30", "density": 0.8127570507531306, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "3b632d53270924b9", "improvement": -0.08186367062158872, "max_boundary_excess": -1.4951723410279072e-06, "max_pair_overlap_depth": -2.2172095294203942e-05, "metric_expression": "4.63186", "metric_symbol": "s", "metric_value": 4.6318636706215885, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.55, "setup": "squinpen", "side": 4.6318636706215885, "solution_path": "data/solutions/generated/squinpen_030_3b632d53270924b9.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b632d53270924b9.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@31", "density": 0.8332446635234546, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "friedman_metric_expression": "4.63041+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.63041, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.63041+", "metric_symbol": "s", "metric_value": 4.63041, "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "4553b8253edc54ee", "improvement": -0.01977349429114028, "max_boundary_excess": -4.6392809673557884e-07, "max_pair_overlap_depth": -4.8013099460675335e-06, "metric_expression": "4.65018", "metric_symbol": "s", "metric_value": 4.650183494291141, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.63041, "setup": "squinpen", "side": 4.650183494291141, "solution_path": "data/solutions/generated/squinpen_031_4553b8253edc54ee.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4553b8253edc54ee.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@32", "density": 0.8340860169571754, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "friedman_metric_expression": "4.70774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.70774, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.70774+", "metric_symbol": "s", "metric_value": 4.70774, "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "b157990acac8fece", "improvement": -0.014467675249534295, "max_boundary_excess": -1.5954744867147025e-06, "max_pair_overlap_depth": -3.644093463414655e-06, "metric_expression": "4.72221", "metric_symbol": "s", "metric_value": 4.7222076752495346, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.70774, "setup": "squinpen", "side": 4.7222076752495346, "solution_path": "data/solutions/generated/squinpen_032_b157990acac8fece.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b157990acac8fece.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@33", "density": 0.8323772382762802, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "friedman_metric_expression": "4.75774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75774, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.75774+", "metric_symbol": "s", "metric_value": 4.75774, "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "84c8eef1219afe3a", "improvement": -0.042604278845473686, "max_boundary_excess": -4.034170035268611e-06, "max_pair_overlap_depth": -3.3231050606596924e-05, "metric_expression": "4.80034", "metric_symbol": "s", "metric_value": 4.800344278845474, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.75774, "setup": "squinpen", "side": 4.800344278845474, "solution_path": "data/solutions/generated/squinpen_033_84c8eef1219afe3a.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/84c8eef1219afe3a.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@34", "density": 0.8367968433764427, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_metric_expression": "4.81817+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.81817, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "01337f10c6d18cd5", "improvement": -0.04147959674377155, "max_boundary_excess": -1.1724733779714692e-06, "max_pair_overlap_depth": -1.9583851482152248e-05, "metric_expression": "4.85965", "metric_symbol": "s", "metric_value": 4.859649596743772, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.81817, "setup": "squinpen", "side": 4.859649596743772, "solution_path": "data/solutions/generated/squinpen_034_01337f10c6d18cd5.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/01337f10c6d18cd5.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@35", "density": 0.8341954934487554, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "friedman_metric_expression": "4.86994+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.86994, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.86994+", "metric_symbol": "s", "metric_value": 4.86994, "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "18582601dada9f12", "improvement": -0.06833892667279251, "max_boundary_excess": -4.548819982417703e-06, "max_pair_overlap_depth": -2.0484902510720104e-05, "metric_expression": "4.93828", "metric_symbol": "s", "metric_value": 4.938278926672792, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.86994, "setup": "squinpen", "side": 4.938278926672792, "solution_path": "data/solutions/generated/squinpen_035_18582601dada9f12.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/18582601dada9f12.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@36", "density": 0.8532713011557852, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "friedman_metric_expression": "4.93902+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93902, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.93902+", "metric_symbol": "s", "metric_value": 4.93902, "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "106a35f9dda2ef3a", "improvement": -0.013009176461455496, "max_boundary_excess": -3.488354007671054e-06, "max_pair_overlap_depth": -9.039025279156121e-06, "metric_expression": "4.95203", "metric_symbol": "s", "metric_value": 4.952029176461456, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.93902, "setup": "squinpen", "side": 4.952029176461456, "solution_path": "data/solutions/generated/squinpen_036_106a35f9dda2ef3a.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/106a35f9dda2ef3a.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@37", "density": 0.8519657791917798, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "friedman_metric_expression": "4.98234+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.98234, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.98234+", "metric_symbol": "s", "metric_value": 4.98234, "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "118ed6265867ee6d", "improvement": -0.041841273572848614, "max_boundary_excess": -2.432358437563004e-06, "max_pair_overlap_depth": -1.088207923216622e-05, "metric_expression": "5.02418", "metric_symbol": "s", "metric_value": 5.024181273572848, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.98234, "setup": "squinpen", "side": 5.024181273572848, "solution_path": "data/solutions/generated/squinpen_037_118ed6265867ee6d.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/118ed6265867ee6d.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@38", "density": 0.8517757106785014, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "friedman_metric_expression": "5.05233+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.05233, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "5.05233+", "metric_symbol": "s", "metric_value": 5.05233, "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "05c73c36e688b1e7", "improvement": -0.03986101653920304, "max_boundary_excess": -4.23968996781929e-06, "max_pair_overlap_depth": -2.3209189968509403e-05, "metric_expression": "5.09219", "metric_symbol": "s", "metric_value": 5.0921910165392035, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.05233, "setup": "squinpen", "side": 5.0921910165392035, "solution_path": "data/solutions/generated/squinpen_038_05c73c36e688b1e7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/05c73c36e688b1e7.svg", "tolerance": 1e-08, "verified": true} {"case": "squinpen@39", "density": 0.8585173524687216, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "5.14034+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.14034, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "5.14034+", "metric_symbol": "s", "metric_value": 5.14034, "reference_text": "s = 5.14034+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.14034+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "id": "d71c022b51de33ef", "improvement": 0.001876469157010341, "max_boundary_excess": -5.100716047053306e-07, "max_pair_overlap_depth": -1.0441692915863499e-06, "n": 39, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 5.14034, "setup": "squinpen", "side": 5.13846353084299, "solution_path": "data/solutions/squinpen_39.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/d71c022b51de33ef.svg", "tolerance": 1e-08, "verified": true} +{"case": "squinpen@40", "density": 0.8631839411542434, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "friedman_metric_expression": "5.17250+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1725, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "5.17250+", "metric_symbol": "s", "metric_value": 5.1725, "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "9fbb25ae252614ca", "improvement": -0.017338380797453645, "max_boundary_excess": -2.5898488984122457e-06, "max_pair_overlap_depth": -1.526607516622036e-05, "metric_expression": "5.18984", "metric_symbol": "s", "metric_value": 5.189838380797454, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.1725, "setup": "squinpen", "side": 5.189838380797454, "solution_path": "data/solutions/generated/squinpen_040_9fbb25ae252614ca.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9fbb25ae252614ca.svg", "tolerance": 1e-08, "verified": true} {"case": "squintri@1", "density": 0.49741240626661626, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1 + 2 / \u221a3 = 2.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "source_image": "ts1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "friedman_source_image": "ts1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bc8215883b0d29fa", "improvement": -0.0007226428063047408, "max_boundary_excess": -4.189638991319711e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "2.15472", "metric_symbol": "s", "metric_value": 2.1547226428063047, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.154, "setup": "squintri", "side": 2.1547226428063047, "solution_path": "data/solutions/generated/squintri_001_bc8215883b0d29fa.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bc8215883b0d29fa.svg", "tolerance": 1e-08, "verified": true} {"case": "squintri@2", "density": 0.4640775964340414, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 2 / \u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "2 + 2 / \u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "source_image": "ts2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "friedman_source_image": "ts2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "9fcb7fc91bdb6f8d", "improvement": -0.000782174335970165, "max_boundary_excess": -6.2952441585539525e-06, "max_pair_overlap_depth": -3.4919698730116744e-05, "metric_expression": "3.15478", "metric_symbol": "s", "metric_value": 3.15478217433597, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.154, "setup": "squintri", "side": 3.15478217433597, "solution_path": "data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9fcb7fc91bdb6f8d.svg", "tolerance": 1e-08, "verified": true} {"case": "squintri@3", "density": 0.6632023535454387, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 / 2 + \u221a3 = 3.232+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.232, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 / 2 + \u221a3 = 3.232+", "metric_symbol": "s", "metric_value": 3.232, "reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "source_image": "ts3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "6a0fd09e2fb037d5", "improvement": -0.00011853663309757678, "max_boundary_excess": -2.0862631378148764e-06, "max_pair_overlap_depth": -4.0896047962125925e-05, "metric_expression": "3.23212", "metric_symbol": "s", "metric_value": 3.232118536633098, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.232, "setup": "squintri", "side": 3.232118536633098, "solution_path": "data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6a0fd09e2fb037d5.svg", "tolerance": 1e-08, "verified": true} @@ -439,6 +583,25 @@ {"case": "squintri@18", "density": 0.7460471945171483, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 4 / \u221a3 = 7.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 4 / \u221a3 = 7.309+", "metric_symbol": "s", "metric_value": 7.309, "reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "7712455ac085d150", "improvement": -0.15553543037287731, "max_boundary_excess": -2.6126528078951194e-06, "max_pair_overlap_depth": -5.242839132613142e-06, "metric_expression": "7.46454", "metric_symbol": "s", "metric_value": 7.4645354303728775, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.309, "setup": "squintri", "side": 7.4645354303728775, "solution_path": "data/solutions/generated/squintri_018_7712455ac085d150.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7712455ac085d150.svg", "tolerance": 1e-08, "verified": true} {"case": "squintri@19", "density": 0.787537700321716, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 2 \u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@19", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 2 \u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "805d1e50c1db2842", "improvement": -0.0003295610354463463, "max_boundary_excess": -3.0609380559736765e-06, "max_pair_overlap_depth": -1.836020690809681e-05, "metric_expression": "7.46433", "metric_symbol": "s", "metric_value": 7.464329561035447, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.464, "setup": "squintri", "side": 7.464329561035447, "solution_path": "data/solutions/generated/squintri_019_805d1e50c1db2842.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/805d1e50c1db2842.svg", "tolerance": 1e-08, "verified": true} {"case": "squintri@20", "density": 0.795657127614163, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "f4d21a73470ce742", "improvement": -0.0010653922379448844, "max_boundary_excess": -1.382631857088383e-07, "max_pair_overlap_depth": -1.1470843414018717e-05, "metric_expression": "7.61907", "metric_symbol": "s", "metric_value": 7.619065392237945, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.618, "setup": "squintri", "side": 7.619065392237945, "solution_path": "data/solutions/generated/squintri_020_f4d21a73470ce742.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f4d21a73470ce742.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@21", "density": 0.8354483980307021, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a2e24601c2557198", "improvement": -0.0010270252659259071, "max_boundary_excess": -2.8035391721895233e-06, "max_pair_overlap_depth": -9.7266150509423e-06, "metric_expression": "7.61903", "metric_symbol": "s", "metric_value": 7.619027025265926, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.618, "setup": "squintri", "side": 7.619027025265926, "solution_path": "data/solutions/generated/squintri_021_a2e24601c2557198.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a2e24601c2557198.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@22", "density": 0.7639711289147475, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "friedman_metric_expression": "7 + 2 / \u221a3 = 8.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@22", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "7 + 2 / \u221a3 = 8.154+", "metric_symbol": "s", "metric_value": 8.154, "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bbb028380d997350", "improvement": -0.00097340620692421, "max_boundary_excess": -2.4334644744109685e-07, "max_pair_overlap_depth": -2.16343036094635e-05, "metric_expression": "8.15497", "metric_symbol": "s", "metric_value": 8.154973406206924, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.154, "setup": "squintri", "side": 8.154973406206924, "solution_path": "data/solutions/generated/squintri_022_bbb028380d997350.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bbb028380d997350.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@23", "density": 0.7550101019412538, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "friedman_metric_expression": "8.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@23", "credit": "David W", "date": "July 2002", "family_updated": "4/28/26", "metric_expression": "8.301+", "metric_symbol": "s", "metric_value": 8.301, "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "23ac4c9fa2eea010", "improvement": -0.08659049275331299, "max_boundary_excess": -4.153049577120555e-06, "max_pair_overlap_depth": -3.895329260372726e-05, "metric_expression": "8.38759", "metric_symbol": "s", "metric_value": 8.387590492753313, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.301, "setup": "squintri", "side": 8.387590492753313, "solution_path": "data/solutions/generated/squintri_023_23ac4c9fa2eea010.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/23ac4c9fa2eea010.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@24", "density": 0.7730739404637164, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "friedman_metric_expression": "6 + 4 / \u221a3 = 8.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@24", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "6 + 4 / \u221a3 = 8.309+", "metric_symbol": "s", "metric_value": 8.309, "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "841c613875887f20", "improvement": -0.15829685349927658, "max_boundary_excess": -3.146275899064303e-06, "max_pair_overlap_depth": -4.677275111941714e-06, "metric_expression": "8.46730", "metric_symbol": "s", "metric_value": 8.467296853499276, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.309, "setup": "squintri", "side": 8.467296853499276, "solution_path": "data/solutions/generated/squintri_024_841c613875887f20.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/841c613875887f20.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@25", "density": 0.7913339513148233, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "friedman_metric_expression": "5 + 2 \u221a3 = 8.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@25", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 2 \u221a3 = 8.464+", "metric_symbol": "s", "metric_value": 8.464, "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b4f5fafd19e47950", "improvement": -0.0776109564627685, "max_boundary_excess": -3.693763855098152e-06, "max_pair_overlap_depth": -1.4039362742357397e-05, "metric_expression": "8.54161", "metric_symbol": "s", "metric_value": 8.541610956462769, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.464, "setup": "squintri", "side": 8.541610956462769, "solution_path": "data/solutions/generated/squintri_025_b4f5fafd19e47950.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4f5fafd19e47950.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@26", "density": 0.790058442487887, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "029d10bebacbb7a8", "improvement": -0.09979689737383879, "max_boundary_excess": -6.192886858462666e-06, "max_pair_overlap_depth": -1.592089192270496e-05, "metric_expression": "8.71780", "metric_symbol": "s", "metric_value": 8.71779689737384, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.618, "setup": "squintri", "side": 8.71779689737384, "solution_path": "data/solutions/generated/squintri_026_029d10bebacbb7a8.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/029d10bebacbb7a8.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@27", "density": 0.8229909021232206, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "d80877f3b5e3e559", "improvement": -0.08630392921703489, "max_boundary_excess": -2.6087107652930556e-07, "max_pair_overlap_depth": -1.4123632457341273e-05, "metric_expression": "8.70430", "metric_symbol": "s", "metric_value": 8.704303929217035, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.618, "setup": "squintri", "side": 8.704303929217035, "solution_path": "data/solutions/generated/squintri_027_d80877f3b5e3e559.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d80877f3b5e3e559.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@28", "density": 0.8400113660191094, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "friedman_metric_expression": "3 + 10 / \u221a3 = 8.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 + 10 / \u221a3 = 8.773+", "metric_symbol": "s", "metric_value": 8.773, "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "0d20b359435ed501", "improvement": -0.0007673944032049462, "max_boundary_excess": -3.0145694937175628e-06, "max_pair_overlap_depth": -1.3941973455278145e-05, "metric_expression": "8.77377", "metric_symbol": "s", "metric_value": 8.773767394403205, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.773, "setup": "squintri", "side": 8.773767394403205, "solution_path": "data/solutions/generated/squintri_028_0d20b359435ed501.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0d20b359435ed501.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@29", "density": 0.7990846545133872, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "friedman_metric_expression": "8 + 2 / \u221a3 = 9.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@29", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "8 + 2 / \u221a3 = 9.154+", "metric_symbol": "s", "metric_value": 9.154, "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3947aab39c0a1a92", "improvement": -0.000872191450978832, "max_boundary_excess": -2.2628787428294703e-06, "max_pair_overlap_depth": -1.875431036468811e-05, "metric_expression": "9.15487", "metric_symbol": "s", "metric_value": 9.154872191450979, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.154, "setup": "squintri", "side": 9.154872191450979, "solution_path": "data/solutions/generated/squintri_029_3947aab39c0a1a92.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3947aab39c0a1a92.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@30", "density": 0.7992784153759376, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "friedman_metric_expression": "9.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@30", "credit": "David W", "date": "July 2002", "family_updated": "4/28/26", "metric_expression": "9.301+", "metric_symbol": "s", "metric_value": 9.301, "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "e0b7505d8b6b1d46", "improvement": -0.009248370808917272, "max_boundary_excess": -2.5690858985090003e-06, "max_pair_overlap_depth": -2.654303096472077e-05, "metric_expression": "9.31025", "metric_symbol": "s", "metric_value": 9.310248370808917, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.301, "setup": "squintri", "side": 9.310248370808917, "solution_path": "data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e0b7505d8b6b1d46.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@31", "density": 0.7864596295366862, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "friedman_metric_expression": "7 + 4 / \u221a3 = 9.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "7 + 4 / \u221a3 = 9.309+", "metric_symbol": "s", "metric_value": 9.309, "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "2fc342f23897d355", "improvement": -0.2319651982792994, "max_boundary_excess": -3.1752928337368137e-06, "max_pair_overlap_depth": -3.6389675686088196e-06, "metric_expression": "9.54097", "metric_symbol": "s", "metric_value": 9.540965198279299, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.309, "setup": "squintri", "side": 9.540965198279299, "solution_path": "data/solutions/generated/squintri_031_2fc342f23897d355.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2fc342f23897d355.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@32", "density": 0.8113508933844216, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "friedman_metric_expression": "6 + 2 \u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@32", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "6 + 2 \u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "5dfb790e771f9b5e", "improvement": -0.07977763160413431, "max_boundary_excess": -1.7955058891584607e-06, "max_pair_overlap_depth": -1.9308988421506967e-06, "metric_expression": "9.54378", "metric_symbol": "s", "metric_value": 9.543777631604135, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.464, "setup": "squintri", "side": 9.543777631604135, "solution_path": "data/solutions/generated/squintri_032_5dfb790e771f9b5e.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5dfb790e771f9b5e.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@33", "density": 0.8101986344458209, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@33", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3a2374dab53b1d0d", "improvement": -0.08064132353736753, "max_boundary_excess": -4.4569871095880175e-06, "max_pair_overlap_depth": -8.479699437735633e-06, "metric_expression": "9.69864", "metric_symbol": "s", "metric_value": 9.698641323537368, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.618, "setup": "squintri", "side": 9.698641323537368, "solution_path": "data/solutions/generated/squintri_033_3a2374dab53b1d0d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3a2374dab53b1d0d.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@34", "density": 0.8485900582279403, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@34", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3661302cdd9d0eb0", "improvement": -0.0012269381751668362, "max_boundary_excess": -4.159334309452278e-06, "max_pair_overlap_depth": -1.741303470170763e-05, "metric_expression": "9.61923", "metric_symbol": "s", "metric_value": 9.619226938175167, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.618, "setup": "squintri", "side": 9.619226938175167, "solution_path": "data/solutions/generated/squintri_034_3661302cdd9d0eb0.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3661302cdd9d0eb0.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@35", "density": 0.819924784927634, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@35", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "767d03b8ae8b30a8", "improvement": -0.15579849696747594, "max_boundary_excess": -4.344704196265019e-07, "max_pair_overlap_depth": -6.54668349642229e-06, "metric_expression": "9.92880", "metric_symbol": "s", "metric_value": 9.928798496967476, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.773, "setup": "squintri", "side": 9.928798496967476, "solution_path": "data/solutions/generated/squintri_035_767d03b8ae8b30a8.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/767d03b8ae8b30a8.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@36", "density": 0.8626567214562272, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@36", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "8dffe8c81eb0e47e", "improvement": -0.044070890619954284, "max_boundary_excess": -4.088894889268143e-06, "max_pair_overlap_depth": -7.423378060700259e-06, "metric_expression": "9.81707", "metric_symbol": "s", "metric_value": 9.817070890619954, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.773, "setup": "squintri", "side": 9.817070890619954, "solution_path": "data/solutions/generated/squintri_036_8dffe8c81eb0e47e.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8dffe8c81eb0e47e.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@37", "density": 0.8285699034870297, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "friedman_metric_expression": "10.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.154, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.154+", "metric_symbol": "s", "metric_value": 10.154, "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "8530be000ac2e9ed", "improvement": -0.0011412138177444575, "max_boundary_excess": -3.3566887422690367e-06, "max_pair_overlap_depth": -1.2239987045248313e-05, "metric_expression": "10.15514", "metric_symbol": "s", "metric_value": 10.155141213817744, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.154, "setup": "squintri", "side": 10.155141213817744, "solution_path": "data/solutions/generated/squintri_037_8530be000ac2e9ed.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8530be000ac2e9ed.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@38", "density": 0.8256293316995508, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "friedman_metric_expression": "10.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.309, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.309+", "metric_symbol": "s", "metric_value": 10.309, "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "896b636f9d899bf5", "improvement": -0.0007687369401132571, "max_boundary_excess": -6.231911901047403e-06, "max_pair_overlap_depth": -1.6045122417374102e-05, "metric_expression": "10.30977", "metric_symbol": "s", "metric_value": 10.309768736940113, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.309, "setup": "squintri", "side": 10.309768736940113, "solution_path": "data/solutions/generated/squintri_038_896b636f9d899bf5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/896b636f9d899bf5.svg", "tolerance": 1e-08, "verified": true} +{"case": "squintri@39", "density": 0.8473139665564875, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "friedman_metric_expression": "10.310+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.31, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.310+", "metric_symbol": "s", "metric_value": 10.31, "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "306f80d621673198", "improvement": -2.7007950082591492e-05, "max_boundary_excess": -5.045618537449805e-06, "max_pair_overlap_depth": -1.8490228973488954e-05, "metric_expression": "10.31003", "metric_symbol": "s", "metric_value": 10.310027007950083, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.31, "setup": "squintri", "side": 10.310027007950083, "solution_path": "data/solutions/generated/squintri_039_306f80d621673198.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/306f80d621673198.svg", "tolerance": 1e-08, "verified": true} {"case": "squintri@40", "density": 0.8436107953893915, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "10.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.465, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.465+", "metric_symbol": "s", "metric_value": 10.465, "reference_text": "s = 10.465+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.465+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "id": "ca1c4f98d45d3360", "improvement": 0.0007377944127142655, "max_boundary_excess": -6.518279549438242e-07, "max_pair_overlap_depth": -1.3221145032105142e-06, "n": 40, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 10.465, "setup": "squintri", "side": 10.464262205587286, "solution_path": "data/solutions/squintri_40.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/ca1c4f98d45d3360.svg", "tolerance": 1e-08, "verified": true} {"case": "triincir@1", "density": 0.41349293224745, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1/\u221a3 = .577+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.577, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@1", "credit": "Trivial", "date": "", "family_updated": "8/31/19", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "r", "metric_value": 0.577, "reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "source_image": "tc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "friedman_source_image": "tc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "49954bfbb560620d", "improvement": -0.00035287974439102143, "max_boundary_excess": -6.775275519510515e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.57735", "metric_symbol": "r", "metric_value": 0.577352879744391, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.577, "setup": "triincir", "side": 1.154705759488782, "solution_path": "data/solutions/generated/triincir_001_49954bfbb560620d.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/49954bfbb560620d.svg", "tolerance": 1e-08, "verified": true} {"case": "triincir@2", "density": 0.3675414068402789, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a3/2 = .866+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.866, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@2", "credit": "Trivial", "date": "", "family_updated": "8/31/19", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "r", "metric_value": 0.866, "reference_text": "r = \u221a3/2 = .866+ | Trivial.", "source_image": "tc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a3/2 = .866+ | Trivial.", "friedman_source_image": "tc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "92f5511b689fe041", "improvement": -3.858712037896339e-05, "max_boundary_excess": -3.072458078845486e-06, "max_pair_overlap_depth": -1.0890566688626091e-05, "metric_expression": "0.86604", "metric_symbol": "r", "metric_value": 0.866038587120379, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.866, "setup": "triincir", "side": 1.732077174240758, "solution_path": "data/solutions/generated/triincir_002_92f5511b689fe041.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92f5511b689fe041.svg", "tolerance": 1e-08, "verified": true} @@ -460,6 +623,17 @@ {"case": "triincir@18", "density": 0.763334042584198, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "8/31/19", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "source_image": "tc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8d495d33c78cce38", "improvement": -0.000828100052461922, "max_boundary_excess": -1.0688499290090192e-06, "max_pair_overlap_depth": -2.7547144944017887e-06, "metric_expression": "1.80283", "metric_symbol": "r", "metric_value": 1.802828100052462, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.802, "setup": "triincir", "side": 3.605656200104924, "solution_path": "data/solutions/generated/triincir_018_8d495d33c78cce38.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8d495d33c78cce38.svg", "tolerance": 1e-08, "verified": true} {"case": "triincir@19", "density": 0.7677097187833641, "friedman_analytical_or_proved": true, "friedman_credit": "Haym Hirsh", "friedman_date": "August 2019", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a(10/3) = 1.825+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.825, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@19", "credit": "Haym Hirsh", "date": "August 2019", "family_updated": "8/31/19", "metric_expression": "\u221a(10/3) = 1.825+", "metric_symbol": "r", "metric_value": 1.825, "reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "source_image": "tc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "friedman_source_image": "tc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "25e61803121deba5", "improvement": -0.021943724350603322, "max_boundary_excess": -6.158152259239102e-07, "max_pair_overlap_depth": -1.4118207399826943e-06, "metric_expression": "1.84694", "metric_symbol": "r", "metric_value": 1.8469437243506033, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.825, "setup": "triincir", "side": 3.6938874487012066, "solution_path": "data/solutions/generated/triincir_019_25e61803121deba5.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/25e61803121deba5.svg", "tolerance": 1e-08, "verified": true} {"case": "triincir@20", "density": 0.7838286390350678, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.874+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.874, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "8/31/19", "metric_expression": "1.874+", "metric_symbol": "r", "metric_value": 1.874, "reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "source_image": "tc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "1217493f9010e655", "improvement": -0.0013391312177313264, "max_boundary_excess": -1.256942872007727e-07, "max_pair_overlap_depth": -1.3401476308239069e-05, "metric_expression": "1.87534", "metric_symbol": "r", "metric_value": 1.8753391312177314, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.874, "setup": "triincir", "side": 3.750678262435463, "solution_path": "data/solutions/generated/triincir_020_1217493f9010e655.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1217493f9010e655.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@21", "density": 0.7807486191939167, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "friedman_metric_expression": "1.910+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.91, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "8/31/19", "metric_expression": "1.910+", "metric_symbol": "r", "metric_value": 1.91, "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "26dd3deb629b6129", "improvement": -0.015437458779652191, "max_boundary_excess": -9.498317063982853e-07, "max_pair_overlap_depth": -2.835010137536287e-06, "metric_expression": "1.92544", "metric_symbol": "r", "metric_value": 1.9254374587796521, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.91, "setup": "triincir", "side": 3.8508749175593042, "solution_path": "data/solutions/generated/triincir_021_26dd3deb629b6129.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/26dd3deb629b6129.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@22", "density": 0.7874465082238514, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "friedman_metric_expression": "1.943+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.943, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@22", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "8/31/19", "metric_expression": "1.943+", "metric_symbol": "r", "metric_value": 1.943, "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "0907be89df20a3ff", "improvement": -0.019348742244891026, "max_boundary_excess": -4.030552757772199e-06, "max_pair_overlap_depth": -1.5844548821419835e-05, "metric_expression": "1.96235", "metric_symbol": "r", "metric_value": 1.962348742244891, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.943, "setup": "triincir", "side": 3.924697484489782, "solution_path": "data/solutions/generated/triincir_022_0907be89df20a3ff.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0907be89df20a3ff.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@23", "density": 0.7918747649774476, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "friedman_metric_expression": "1.988+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.988, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@23", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "8/31/19", "metric_expression": "1.988+", "metric_symbol": "r", "metric_value": 1.988, "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "973cadfcac9f0399", "improvement": -0.012833950693412532, "max_boundary_excess": -2.3604816288269603e-06, "max_pair_overlap_depth": -6.566732802859576e-06, "metric_expression": "2.00083", "metric_symbol": "r", "metric_value": 2.0008339506934125, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.988, "setup": "triincir", "side": 4.001667901386825, "solution_path": "data/solutions/generated/triincir_023_973cadfcac9f0399.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/973cadfcac9f0399.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@24", "density": 0.77037708306075, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@24", "credit": "Trivial", "date": "", "family_updated": "8/31/19", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "tc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "tc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "9ebf7fbae73f62a7", "improvement": -0.07218881407517408, "max_boundary_excess": -1.2456668625482337e-06, "max_pair_overlap_depth": -4.316070905119318e-07, "metric_expression": "2.07219", "metric_symbol": "r", "metric_value": 2.072188814075174, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triincir", "side": 4.144377628150348, "solution_path": "data/solutions/generated/triincir_024_9ebf7fbae73f62a7.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9ebf7fbae73f62a7.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@25", "density": 0.814798554480224, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "friedman_metric_expression": "2.055+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.055, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@25", "credit": "David W", "date": "July 2005", "family_updated": "8/31/19", "metric_expression": "2.055+", "metric_symbol": "r", "metric_value": 2.055, "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "460bfc63493e0a99", "improvement": -0.0014599742843675045, "max_boundary_excess": -5.499842621325968e-07, "max_pair_overlap_depth": -5.533591762807433e-06, "metric_expression": "2.05646", "metric_symbol": "r", "metric_value": 2.0564599742843677, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.055, "setup": "triincir", "side": 4.112919948568735, "solution_path": "data/solutions/generated/triincir_025_460bfc63493e0a99.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/460bfc63493e0a99.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@26", "density": 0.763639473601239, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "friedman_metric_expression": "2.109+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.109, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@26", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "8/31/19", "metric_expression": "2.109+", "metric_symbol": "r", "metric_value": 2.109, "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "297d48c1e4300be9", "improvement": -0.057296364393150334, "max_boundary_excess": -2.064436773085987e-06, "max_pair_overlap_depth": -1.3195031345336616e-07, "metric_expression": "2.16630", "metric_symbol": "r", "metric_value": 2.1662963643931503, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.109, "setup": "triincir", "side": 4.332592728786301, "solution_path": "data/solutions/generated/triincir_026_297d48c1e4300be9.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/297d48c1e4300be9.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@27", "density": 0.791482135514487, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "friedman_metric_expression": "2.138+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.138, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@27", "credit": "David W", "date": "July 2005", "family_updated": "8/31/19", "metric_expression": "2.138+", "metric_symbol": "r", "metric_value": 2.138, "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "0b682f2ff7f493f4", "improvement": -0.03038655259456835, "max_boundary_excess": -8.100188688686671e-07, "max_pair_overlap_depth": -1.2480037501427788e-05, "metric_expression": "2.16839", "metric_symbol": "r", "metric_value": 2.1683865525945683, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.138, "setup": "triincir", "side": 4.3367731051891365, "solution_path": "data/solutions/generated/triincir_027_0b682f2ff7f493f4.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0b682f2ff7f493f4.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@28", "density": 0.7833608666700476, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "friedman_metric_expression": "2.191+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.191, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@28", "credit": "David W", "date": "July 2005", "family_updated": "8/31/19", "metric_expression": "2.191+", "metric_symbol": "r", "metric_value": 2.191, "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "f7e451634cc50a5c", "improvement": -0.028593586242025903, "max_boundary_excess": -3.334899561835414e-06, "max_pair_overlap_depth": -1.391899336167235e-05, "metric_expression": "2.21959", "metric_symbol": "r", "metric_value": 2.2195935862420257, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.191, "setup": "triincir", "side": 4.4391871724840515, "solution_path": "data/solutions/generated/triincir_028_f7e451634cc50a5c.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f7e451634cc50a5c.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@29", "density": 0.8182348688742829, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "friedman_metric_expression": "2.215+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.215, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@29", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "8/31/19", "metric_expression": "2.215+", "metric_symbol": "r", "metric_value": 2.215, "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "73bcaf90b9fd2226", "improvement": 0.004780586805306797, "max_boundary_excess": -3.1271053040349273e-06, "max_pair_overlap_depth": -1.2019034158372577e-05, "metric_expression": "2.21022", "metric_symbol": "r", "metric_value": 2.210219413194693, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.215, "setup": "triincir", "side": 4.420438826389386, "solution_path": "data/solutions/generated/triincir_029_73bcaf90b9fd2226.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/73bcaf90b9fd2226.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@30", "density": 0.7948627844239105, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "friedman_metric_expression": "2.258+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.258, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@30", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "8/31/19", "metric_expression": "2.258+", "metric_symbol": "r", "metric_value": 2.258, "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "05c2ceb22d6802af", "improvement": -0.022814299780184122, "max_boundary_excess": -3.282499053458565e-06, "max_pair_overlap_depth": -7.525015305542837e-06, "metric_expression": "2.28081", "metric_symbol": "r", "metric_value": 2.280814299780184, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.258, "setup": "triincir", "side": 4.561628599560368, "solution_path": "data/solutions/generated/triincir_030_05c2ceb22d6802af.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/05c2ceb22d6802af.svg", "tolerance": 1e-08, "verified": true} +{"case": "triincir@31", "density": 0.8077135574878077, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "friedman_metric_expression": "2.272+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.272, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@31", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "8/31/19", "metric_expression": "2.272+", "metric_symbol": "r", "metric_value": 2.272, "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "d099d25f47dd541c", "improvement": -0.027998444456735605, "max_boundary_excess": -5.317100407520314e-06, "max_pair_overlap_depth": -1.0941201894709707e-05, "metric_expression": "2.30000", "metric_symbol": "r", "metric_value": 2.2999984444567354, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.272, "setup": "triincir", "side": 4.599996888913471, "solution_path": "data/solutions/generated/triincir_031_d099d25f47dd541c.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d099d25f47dd541c.svg", "tolerance": 1e-08, "verified": true} {"case": "triindom@1", "density": 0.2886702903701934, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@1", "credit": "Trivial", "date": "", "family_updated": "4/4/26", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "37b1dca676a779e3", "improvement": -7.266428382335377e-06, "max_boundary_excess": -2.4019537994690587e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.86603", "metric_symbol": "s", "metric_value": 0.8660326702128209, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320653404256419, "solution_path": "data/solutions/generated/triindom_001_37b1dca676a779e3.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/37b1dca676a779e3.svg", "tolerance": 1e-08, "verified": true} {"case": "triindom@2", "density": 0.5773351362696808, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@2", "credit": "Trivial", "date": "", "family_updated": "4/4/26", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "31518429031d2b51", "improvement": -1.1349913078717577e-05, "max_boundary_excess": -6.727531273176268e-07, "max_pair_overlap_depth": -0.13184728443338464, "metric_expression": "0.86604", "metric_symbol": "s", "metric_value": 0.8660367536975173, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320735073950346, "solution_path": "data/solutions/generated/triindom_002_31518429031d2b51.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/31518429031d2b51.svg", "tolerance": 1e-08, "verified": true} {"case": "triindom@3", "density": 0.6931800833949334, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": ".96796+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.96796, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/4/26", "metric_expression": ".96796+", "metric_symbol": "s", "metric_value": 0.96796, "reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "b10402bd10926cd1", "improvement": -3.454421484250236e-05, "max_boundary_excess": -1.601436348197538e-06, "max_pair_overlap_depth": -2.0206571078401625e-05, "metric_expression": "0.96799", "metric_symbol": "s", "metric_value": 0.9679945442148425, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.96796, "setup": "triindom", "side": 1.935989088429685, "solution_path": "data/solutions/generated/triindom_003_b10402bd10926cd1.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b10402bd10926cd1.svg", "tolerance": 1e-08, "verified": true} @@ -500,8 +674,25 @@ {"case": "triinhex@18", "density": 0.8297080120836304, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "17/9 = 1.888+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.888, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@18", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "4/29/26", "metric_expression": "17/9 = 1.888+", "metric_symbol": "s", "metric_value": 1.888, "reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "6c5f13d522480054", "improvement": -0.013507249150880973, "max_boundary_excess": -1.7176270484116662e-06, "max_pair_overlap_depth": -2.0474118108848582e-05, "metric_expression": "1.90151", "metric_symbol": "s", "metric_value": 1.9015072491508809, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.888, "setup": "triinhex", "side": 1.9015072491508809, "solution_path": "data/solutions/generated/triinhex_018_6c5f13d522480054.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6c5f13d522480054.svg", "tolerance": 1e-08, "verified": true} {"case": "triinhex@19", "density": 0.8252355857972508, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Adri\u00e1n Nieto", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.953+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.953, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@19", "credit": "Alex Adri\u00e1n Nieto", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "1.953+", "metric_symbol": "s", "metric_value": 1.953, "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dca0a965c4496e80", "improvement": -0.005899708509202517, "max_boundary_excess": -1.4140126041781837e-06, "max_pair_overlap_depth": -4.097714423223486e-06, "metric_expression": "1.95890", "metric_symbol": "s", "metric_value": 1.9588997085092026, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.953, "setup": "triinhex", "side": 1.9588997085092026, "solution_path": "data/solutions/generated/triinhex_019_dca0a965c4496e80.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dca0a965c4496e80.svg", "tolerance": 1e-08, "verified": true} {"case": "triinhex@20", "density": 0.84905335156007, "friedman_analytical_or_proved": false, "friedman_credit": "Aaden Abraham", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.97591+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.97591, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@20", "credit": "Aaden Abraham", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "1.97591+", "metric_symbol": "s", "metric_value": 1.97591, "reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8af6938cdb16e6d8", "improvement": -0.005488739222003547, "max_boundary_excess": -2.9749927869818494e-07, "max_pair_overlap_depth": -5.967603292744705e-06, "metric_expression": "1.98140", "metric_symbol": "s", "metric_value": 1.9813987392220036, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.97591, "setup": "triinhex", "side": 1.9813987392220036, "solution_path": "data/solutions/generated/triinhex_020_8af6938cdb16e6d8.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8af6938cdb16e6d8.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@21", "density": 0.8749527320468723, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "friedman_metric_expression": "1.99878+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.99878, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "1.99878+", "metric_symbol": "s", "metric_value": 1.99878, "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "96f74df50573bb81", "improvement": -0.0012740227066210252, "max_boundary_excess": -8.545179480294009e-07, "max_pair_overlap_depth": -6.765642482919887e-06, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.000054022706621, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.99878, "setup": "triinhex", "side": 2.000054022706621, "solution_path": "data/solutions/generated/triinhex_021_96f74df50573bb81.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/96f74df50573bb81.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@22", "density": 0.9166150664792877, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@22", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "38182a59461da74e", "improvement": -5.629349013291929e-05, "max_boundary_excess": -4.91184500961419e-07, "max_pair_overlap_depth": -9.942352799940934e-07, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.000056293490133, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056293490133, "solution_path": "data/solutions/generated/triinhex_022_38182a59461da74e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/38182a59461da74e.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@23", "density": 0.958278890368788, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@23", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dcd331994270a997", "improvement": -5.681247061106731e-05, "max_boundary_excess": -1.0734329507489061e-06, "max_pair_overlap_depth": -9.41664729126046e-06, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.000056812470611, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056812470611, "solution_path": "data/solutions/generated/triinhex_023_dcd331994270a997.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dcd331994270a997.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@24", "density": 0.9999420291406096, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@24", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "13936a08bfd4d152", "improvement": -5.7973379977482864e-05, "max_boundary_excess": -1.3635152509087512e-06, "max_pair_overlap_depth": -3.8859579855957235e-06, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.0000579733799775, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.0000579733799775, "solution_path": "data/solutions/generated/triinhex_024_13936a08bfd4d152.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/13936a08bfd4d152.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@25", "density": 0.8871759236838516, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "friedman_metric_expression": "13/6 = 2.166+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.166, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "13/6 = 2.166+", "metric_symbol": "s", "metric_value": 2.166, "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "71a7801cfb4a8d31", "improvement": -0.0011526610601886311, "max_boundary_excess": -6.780494307380179e-07, "max_pair_overlap_depth": -1.3308976067882838e-06, "metric_expression": "2.16715", "metric_symbol": "s", "metric_value": 2.1671526610601886, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.166, "setup": "triinhex", "side": 2.1671526610601886, "solution_path": "data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/71a7801cfb4a8d31.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@26", "density": 0.878430458154361, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "friedman_metric_expression": "2.21991+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.21991, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.21991+", "metric_symbol": "s", "metric_value": 2.21991, "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "658d7f93b604b663", "improvement": -0.0011349903788469007, "max_boundary_excess": -6.149641376243232e-07, "max_pair_overlap_depth": -5.41804289733161e-06, "metric_expression": "2.22104", "metric_symbol": "s", "metric_value": 2.221044990378847, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.21991, "setup": "triinhex", "side": 2.221044990378847, "solution_path": "data/solutions/generated/triinhex_026_658d7f93b604b663.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/658d7f93b604b663.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@27", "density": 0.8328322571122685, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "friedman_metric_expression": "2.29541+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29541, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.29541+", "metric_symbol": "s", "metric_value": 2.29541, "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "11ad91d5c6b8788e", "improvement": -0.029078960495372286, "max_boundary_excess": -8.325360180907825e-06, "max_pair_overlap_depth": -2.435631066832755e-06, "metric_expression": "2.32449", "metric_symbol": "s", "metric_value": 2.3244889604953722, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.29541, "setup": "triinhex", "side": 2.3244889604953722, "solution_path": "data/solutions/generated/triinhex_027_11ad91d5c6b8788e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/11ad91d5c6b8788e.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@28", "density": 0.8335778928127813, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "friedman_metric_expression": "2.32289+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32289, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.32289+", "metric_symbol": "s", "metric_value": 2.32289, "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "2b319174d63885b4", "improvement": -0.0431947496358025, "max_boundary_excess": -3.599330529801011e-06, "max_pair_overlap_depth": -6.859690785454564e-06, "metric_expression": "2.36608", "metric_symbol": "s", "metric_value": 2.3660847496358026, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.32289, "setup": "triinhex", "side": 2.3660847496358026, "solution_path": "data/solutions/generated/triinhex_028_2b319174d63885b4.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2b319174d63885b4.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@29", "density": 0.837502602292776, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "friedman_metric_expression": "7/3 = 2.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.333, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "64c6a497fdd4bc1d", "improvement": -0.06931687053876034, "max_boundary_excess": -5.555832025645621e-06, "max_pair_overlap_depth": -3.7939764052641323e-06, "metric_expression": "2.40232", "metric_symbol": "s", "metric_value": 2.4023168705387605, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.333, "setup": "triinhex", "side": 2.4023168705387605, "solution_path": "data/solutions/generated/triinhex_029_64c6a497fdd4bc1d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/64c6a497fdd4bc1d.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@30", "density": 0.8237939342513431, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "friedman_metric_expression": "19/8 = 2.375", "friedman_metric_symbol": "s", "friedman_metric_value": 2.375, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "19/8 = 2.375", "metric_symbol": "s", "metric_value": 2.375, "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "11d17f9e12268b02", "improvement": -0.08863126687001355, "max_boundary_excess": -2.046588857940021e-06, "max_pair_overlap_depth": -2.8430880139040937e-06, "metric_expression": "2.46363", "metric_symbol": "s", "metric_value": 2.4636312668700135, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.375, "setup": "triinhex", "side": 2.4636312668700135, "solution_path": "data/solutions/generated/triinhex_030_11d17f9e12268b02.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/11d17f9e12268b02.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@31", "density": 0.8505895807478101, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "friedman_metric_expression": "12/5 = 2.400", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "12/5 = 2.400", "metric_symbol": "s", "metric_value": 2.4, "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "1ce8108c850d5941", "improvement": -0.06459289672266566, "max_boundary_excess": -7.67227682312255e-06, "max_pair_overlap_depth": -3.638067419098334e-06, "metric_expression": "2.46459", "metric_symbol": "s", "metric_value": 2.4645928967226656, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.4, "setup": "triinhex", "side": 2.4645928967226656, "solution_path": "data/solutions/generated/triinhex_031_1ce8108c850d5941.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1ce8108c850d5941.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@32", "density": 0.8767870241121234, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "friedman_metric_expression": "2.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.465, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.465+", "metric_symbol": "s", "metric_value": 2.465, "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8674581436e5e74d", "improvement": -0.0013363682337788063, "max_boundary_excess": -6.925122041572899e-07, "max_pair_overlap_depth": -1.2807310418028184e-06, "metric_expression": "2.46634", "metric_symbol": "s", "metric_value": 2.4663363682337787, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.465, "setup": "triinhex", "side": 2.4663363682337787, "solution_path": "data/solutions/generated/triinhex_032_8674581436e5e74d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8674581436e5e74d.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@33", "density": 0.8799443949567897, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "friedman_metric_expression": "2.498+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.498, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.498+", "metric_symbol": "s", "metric_value": 2.498, "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "5b836a27d2bb958c", "improvement": -0.00207898817969987, "max_boundary_excess": -2.8634496562140136e-06, "max_pair_overlap_depth": -5.829272115620565e-06, "metric_expression": "2.50008", "metric_symbol": "s", "metric_value": 2.5000789881797, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.498, "setup": "triinhex", "side": 2.5000789881797, "solution_path": "data/solutions/generated/triinhex_033_5b836a27d2bb958c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5b836a27d2bb958c.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@34", "density": 0.9066102013779274, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a712744ff3b5bcc9", "improvement": -7.7851001305973e-05, "max_boundary_excess": -1.2753913921730298e-06, "max_pair_overlap_depth": -7.960301433351802e-06, "metric_expression": "2.50008", "metric_symbol": "s", "metric_value": 2.500077851001306, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.500077851001306, "solution_path": "data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a712744ff3b5bcc9.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@35", "density": 0.8784557475555014, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "6c433acba2e3b71c", "improvement": -0.07690526384601659, "max_boundary_excess": -2.8573318260367013e-06, "max_pair_overlap_depth": -2.7042986540104508e-06, "metric_expression": "2.57691", "metric_symbol": "s", "metric_value": 2.5769052638460166, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.5769052638460166, "solution_path": "data/solutions/generated/triinhex_035_6c433acba2e3b71c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6c433acba2e3b71c.svg", "tolerance": 1e-08, "verified": true} {"case": "triinhex@36", "density": 0.893589353430048, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.592+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.592, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.592+", "metric_symbol": "s", "metric_value": 2.592, "reference_text": "s = 2.592+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.592+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "id": "e4e0e01451d6ca30", "improvement": 0.0007660070914519146, "max_boundary_excess": -3.7601717225028787e-07, "max_pair_overlap_depth": -3.324194429499272e-06, "n": 36, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 2.592, "setup": "triinhex", "side": 2.591233992908548, "solution_path": "data/solutions/triinhex_36.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/e4e0e01451d6ca30.svg", "tolerance": 1e-08, "verified": true} {"case": "triinhex@37", "density": 0.8987469977236169, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.655+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.655, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.655+", "metric_symbol": "s", "metric_value": 2.655, "reference_text": "s = 2.655+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.655+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "id": "c1697d9445319eaa", "improvement": 0.035571728604908426, "max_boundary_excess": -1.2650118661675414e-07, "max_pair_overlap_depth": -4.4643045216119503e-07, "n": 37, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 2.655, "setup": "triinhex", "side": 2.6194282713950914, "solution_path": "data/solutions/triinhex_37.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/c1697d9445319eaa.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@38", "density": 0.8907392561961515, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "76fd196e8c79a5c9", "improvement": -0.0004956329108489754, "max_boundary_excess": -3.7850003642140776e-06, "max_pair_overlap_depth": -3.863933217385096e-06, "metric_expression": "2.66650", "metric_symbol": "s", "metric_value": 2.666495632910849, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.666, "setup": "triinhex", "side": 2.666495632910849, "solution_path": "data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/76fd196e8c79a5c9.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinhex@39", "density": 0.8833522738592235, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "cf1c7ccbe8f975b2", "improvement": -0.04662470457951118, "max_boundary_excess": -2.2386896785242527e-06, "max_pair_overlap_depth": -9.826603503571008e-06, "metric_expression": "2.71262", "metric_symbol": "s", "metric_value": 2.712624704579511, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.666, "setup": "triinhex", "side": 2.712624704579511, "solution_path": "data/solutions/generated/triinhex_039_cf1c7ccbe8f975b2.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cf1c7ccbe8f975b2.svg", "tolerance": 1e-08, "verified": true} {"case": "triinhex@40", "density": 0.9036048260198691, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.719+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.719, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.719+", "metric_symbol": "s", "metric_value": 2.719, "reference_text": "s = 2.719+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.719+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "id": "0ebde2f6b4b26d2b", "improvement": 0.002779018588611848, "max_boundary_excess": -5.817255795307e-07, "max_pair_overlap_depth": -1.0085947836913078e-06, "n": 40, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 2.719, "setup": "triinhex", "side": 2.716220981411388, "solution_path": "data/solutions/triinhex_40.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/0ebde2f6b4b26d2b.svg", "tolerance": 1e-08, "verified": true} {"case": "triinoct@1", "density": 0.4152122478191623, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".46470+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.4647, "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@1", "credit": "Trivial", "date": "", "family_updated": "3/22/26", "metric_expression": ".46470+", "metric_symbol": "s", "metric_value": 0.4647, "reference_text": "s = .46470+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .46470+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "92c66f395ff03ab9", "improvement": -4.251046545072912e-05, "max_boundary_excess": -2.3282842257895898e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.46474", "metric_symbol": "s", "metric_value": 0.46474251046545073, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.4647, "setup": "triinoct", "side": 0.46474251046545073, "solution_path": "data/solutions/generated/triinoct_001_92c66f395ff03ab9.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92c66f395ff03ab9.svg", "tolerance": 1e-08, "verified": true} {"case": "triinoct@2", "density": 0.40823825072318354, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.66282, "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@2", "credit": "Trivial", "date": "", "family_updated": "3/22/26", "metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "metric_symbol": "s", "metric_value": 0.66282, "reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "5706480ca6648c20", "improvement": -1.5298424264065247e-05, "max_boundary_excess": -4.197393779037103e-06, "max_pair_overlap_depth": -5.033792755404498e-07, "metric_expression": "0.66284", "metric_symbol": "s", "metric_value": 0.662835298424264, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.66282, "setup": "triinoct", "side": 0.662835298424264, "solution_path": "data/solutions/generated/triinoct_002_5706480ca6648c20.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5706480ca6648c20.svg", "tolerance": 1e-08, "verified": true} @@ -523,6 +714,16 @@ {"case": "triinoct@18", "density": 0.7984879014669996, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.41836+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.41836, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.41836+", "metric_symbol": "s", "metric_value": 1.41836, "reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "8e956085d3bcc5e4", "improvement": -0.00347617639937825, "max_boundary_excess": -2.3654127749911342e-06, "max_pair_overlap_depth": -6.1952459529668324e-06, "metric_expression": "1.42184", "metric_symbol": "s", "metric_value": 1.4218361763993783, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.41836, "setup": "triinoct", "side": 1.4218361763993783, "solution_path": "data/solutions/generated/triinoct_018_8e956085d3bcc5e4.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8e956085d3bcc5e4.svg", "tolerance": 1e-08, "verified": true} {"case": "triinoct@19", "density": 0.785495925696758, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.46749+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.46749, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.46749+", "metric_symbol": "s", "metric_value": 1.46749, "reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "b85e7f72b874a80d", "improvement": -0.005338941628411087, "max_boundary_excess": -1.1956920861702103e-06, "max_pair_overlap_depth": -5.584055034923985e-06, "metric_expression": "1.47283", "metric_symbol": "s", "metric_value": 1.472828941628411, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.46749, "setup": "triinoct", "side": 1.472828941628411, "solution_path": "data/solutions/generated/triinoct_019_b85e7f72b874a80d.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b85e7f72b874a80d.svg", "tolerance": 1e-08, "verified": true} {"case": "triinoct@20", "density": 0.7943876162475321, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.49832+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.49832, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.49832+", "metric_symbol": "s", "metric_value": 1.49832, "reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "5dc5edf6bbc42f57", "improvement": -0.004289888994578384, "max_boundary_excess": -1.8456961687288941e-06, "max_pair_overlap_depth": -7.334356214305782e-06, "metric_expression": "1.50261", "metric_symbol": "s", "metric_value": 1.5026098889945785, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.49832, "setup": "triinoct", "side": 1.5026098889945785, "solution_path": "data/solutions/generated/triinoct_020_5dc5edf6bbc42f57.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5dc5edf6bbc42f57.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@21", "density": 0.8006209623113996, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "friedman_metric_expression": "1.52615+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.52615, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.52615+", "metric_symbol": "s", "metric_value": 1.52615, "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "550235b8e64c906b", "improvement": -0.007561402736510292, "max_boundary_excess": -3.854617439163859e-07, "max_pair_overlap_depth": -1.236860211395463e-05, "metric_expression": "1.53371", "metric_symbol": "s", "metric_value": 1.5337114027365102, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.52615, "setup": "triinoct", "side": 1.5337114027365102, "solution_path": "data/solutions/generated/triinoct_021_550235b8e64c906b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/550235b8e64c906b.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@22", "density": 0.8117485196689109, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "friedman_metric_expression": "1.55545+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.55545, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.55545+", "metric_symbol": "s", "metric_value": 1.55545, "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "a1924650c6f006ea", "improvement": -0.0035570002935343403, "max_boundary_excess": -4.3062927716738536e-06, "max_pair_overlap_depth": -1.800963083109508e-06, "metric_expression": "1.55901", "metric_symbol": "s", "metric_value": 1.5590070002935343, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.55545, "setup": "triinoct", "side": 1.5590070002935343, "solution_path": "data/solutions/generated/triinoct_022_a1924650c6f006ea.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a1924650c6f006ea.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@23", "density": 0.8210902170609379, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "friedman_metric_expression": "1.58458+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.58458, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.58458+", "metric_symbol": "s", "metric_value": 1.58458, "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4ca1a825a22b1f04", "improvement": -0.0003714249913302492, "max_boundary_excess": -8.321393677649287e-06, "max_pair_overlap_depth": -1.5960535921788477e-06, "metric_expression": "1.58495", "metric_symbol": "s", "metric_value": 1.5849514249913303, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.58458, "setup": "triinoct", "side": 1.5849514249913303, "solution_path": "data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4ca1a825a22b1f04.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@24", "density": 0.8373304168984339, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "friedman_metric_expression": "1.60261+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.60261, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.60261+", "metric_symbol": "s", "metric_value": 1.60261, "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e197b92ecac28558", "improvement": -0.0006526103809141315, "max_boundary_excess": -2.085338835265612e-06, "max_pair_overlap_depth": -9.98840296584369e-06, "metric_expression": "1.60326", "metric_symbol": "s", "metric_value": 1.6032626103809142, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.60261, "setup": "triinoct", "side": 1.6032626103809142, "solution_path": "data/solutions/generated/triinoct_024_e197b92ecac28558.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e197b92ecac28558.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@25", "density": 0.8206390570044901, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "friedman_metric_expression": "1.63797+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.63797, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.63797+", "metric_symbol": "s", "metric_value": 1.63797, "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4e1b861b138850ae", "improvement": -0.014910250491960486, "max_boundary_excess": -2.6877619511415554e-06, "max_pair_overlap_depth": -7.2555966788498405e-06, "metric_expression": "1.65288", "metric_symbol": "s", "metric_value": 1.6528802504919604, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.63797, "setup": "triinoct", "side": 1.6528802504919604, "solution_path": "data/solutions/generated/triinoct_025_4e1b861b138850ae.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4e1b861b138850ae.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@26", "density": 0.8149644565721081, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "friedman_metric_expression": "1.67666+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.67666, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.67666+", "metric_symbol": "s", "metric_value": 1.67666, "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "cbcb6c755dc046de", "improvement": -0.014812017272631595, "max_boundary_excess": -3.687228372083238e-07, "max_pair_overlap_depth": -1.2896587116006941e-06, "metric_expression": "1.69147", "metric_symbol": "s", "metric_value": 1.6914720172726316, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.67666, "setup": "triinoct", "side": 1.6914720172726316, "solution_path": "data/solutions/generated/triinoct_026_cbcb6c755dc046de.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cbcb6c755dc046de.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@27", "density": 0.8010680431479879, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "friedman_metric_expression": "1.70882+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.70882, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.70882+", "metric_symbol": "s", "metric_value": 1.70882, "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "836b5a3b2c412e9b", "improvement": -0.029759907189525592, "max_boundary_excess": -9.248042691084391e-07, "max_pair_overlap_depth": -7.87865755902395e-06, "metric_expression": "1.73858", "metric_symbol": "s", "metric_value": 1.7385799071895256, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.70882, "setup": "triinoct", "side": 1.7385799071895256, "solution_path": "data/solutions/generated/triinoct_027_836b5a3b2c412e9b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/836b5a3b2c412e9b.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@28", "density": 0.8165576484730356, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "friedman_metric_expression": "1.73954+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73954, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.73954+", "metric_symbol": "s", "metric_value": 1.73954, "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "728bf65e8a483e5e", "improvement": -0.014070219094066916, "max_boundary_excess": -4.0057635728717315e-07, "max_pair_overlap_depth": -1.0036991463513445e-05, "metric_expression": "1.75361", "metric_symbol": "s", "metric_value": 1.753610219094067, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.73954, "setup": "triinoct", "side": 1.753610219094067, "solution_path": "data/solutions/generated/triinoct_028_728bf65e8a483e5e.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/728bf65e8a483e5e.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@29", "density": 0.8071992437047276, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "friedman_metric_expression": "1.75576+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.75576, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.75576+", "metric_symbol": "s", "metric_value": 1.75576, "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f6d5bdc33f1fd083", "improvement": -0.03920549021863984, "max_boundary_excess": -2.872640643928272e-06, "max_pair_overlap_depth": -2.128542299273395e-05, "metric_expression": "1.79497", "metric_symbol": "s", "metric_value": 1.7949654902186398, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.75576, "setup": "triinoct", "side": 1.7949654902186398, "solution_path": "data/solutions/generated/triinoct_029_f6d5bdc33f1fd083.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f6d5bdc33f1fd083.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinoct@30", "density": 0.8241852827166171, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "friedman_metric_expression": "1.78101+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.78101, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.78101+", "metric_symbol": "s", "metric_value": 1.78101, "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "55871e661d418192", "improvement": -0.02573007339812161, "max_boundary_excess": -9.550198166939913e-07, "max_pair_overlap_depth": -3.435684308383813e-06, "metric_expression": "1.80674", "metric_symbol": "s", "metric_value": 1.8067400733981216, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.78101, "setup": "triinoct", "side": 1.8067400733981216, "solution_path": "data/solutions/generated/triinoct_030_55871e661d418192.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/55871e661d418192.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@1", "density": 0.4121951299103008, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": ".781+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.781, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": ".781+", "metric_symbol": "s", "metric_value": 0.781, "reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6d3af7533c544064", "improvement": -0.0004017935524769367, "max_boundary_excess": -5.010333690326338e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78140", "metric_symbol": "s", "metric_value": 0.781401793552477, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.781, "setup": "triinpen", "side": 0.781401793552477, "solution_path": "data/solutions/generated/triinpen_001_6d3af7533c544064.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6d3af7533c544064.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@2", "density": 0.4392461428307515, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.070+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.07, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "1.070+", "metric_symbol": "s", "metric_value": 1.07, "reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "eebb278fed1959e5", "improvement": -0.0005004432401414238, "max_boundary_excess": -7.540244142797655e-06, "max_pair_overlap_depth": -4.677606255020384e-06, "metric_expression": "1.07050", "metric_symbol": "s", "metric_value": 1.0705004432401415, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.07, "setup": "triinpen", "side": 1.0705004432401415, "solution_path": "data/solutions/generated/triinpen_002_eebb278fed1959e5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/eebb278fed1959e5.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@3", "density": 0.5773621092377123, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.143+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.143, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@3", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "4/29/26", "metric_expression": "1.143+", "metric_symbol": "s", "metric_value": 1.143, "reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6ec3c588fb678646", "improvement": -0.0005688574140261249, "max_boundary_excess": -1.4403665141977852e-06, "max_pair_overlap_depth": -4.738354987265936e-06, "metric_expression": "1.14357", "metric_symbol": "s", "metric_value": 1.1435688574140261, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.143, "setup": "triinpen", "side": 1.1435688574140261, "solution_path": "data/solutions/generated/triinpen_003_6ec3c588fb678646.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6ec3c588fb678646.svg", "tolerance": 1e-08, "verified": true} @@ -543,8 +744,25 @@ {"case": "triinpen@18", "density": 0.8386266626517904, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.29382+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29382, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.29382+", "metric_symbol": "s", "metric_value": 2.29382, "reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "286d64d1342c9a9f", "improvement": -0.0304027693812583, "max_boundary_excess": -2.3683231734867957e-06, "max_pair_overlap_depth": -9.23929068963325e-06, "metric_expression": "2.32422", "metric_symbol": "s", "metric_value": 2.3242227693812585, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.29382, "setup": "triinpen", "side": 2.3242227693812585, "solution_path": "data/solutions/generated/triinpen_018_286d64d1342c9a9f.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/286d64d1342c9a9f.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@19", "density": 0.831205150275822, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "5f0b9905f54e5f87", "improvement": -0.05454858293536624, "max_boundary_excess": -1.8779608876987526e-06, "max_pair_overlap_depth": -1.5527720347900675e-05, "metric_expression": "2.39855", "metric_symbol": "s", "metric_value": 2.398548582935366, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.398548582935366, "solution_path": "data/solutions/generated/triinpen_019_5f0b9905f54e5f87.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5f0b9905f54e5f87.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@20", "density": 0.8487102106795418, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.43350+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4335, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.43350+", "metric_symbol": "s", "metric_value": 2.4335, "reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "760faebc4d0b131b", "improvement": -0.001848490502489586, "max_boundary_excess": -7.176183787084704e-07, "max_pair_overlap_depth": -8.807499014995557e-06, "metric_expression": "2.43535", "metric_symbol": "s", "metric_value": 2.4353484905024896, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.4335, "setup": "triinpen", "side": 2.4353484905024896, "solution_path": "data/solutions/generated/triinpen_020_760faebc4d0b131b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/760faebc4d0b131b.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@21", "density": 0.8589998748063701, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "friedman_metric_expression": "2.479+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.479, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.479+", "metric_symbol": "s", "metric_value": 2.479, "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "115c20fad199fe9d", "improvement": -0.0014982727861765355, "max_boundary_excess": -2.811024693767028e-06, "max_pair_overlap_depth": -2.8209410938284663e-06, "metric_expression": "2.48050", "metric_symbol": "s", "metric_value": 2.4804982727861766, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.479, "setup": "triinpen", "side": 2.4804982727861766, "solution_path": "data/solutions/generated/triinpen_021_115c20fad199fe9d.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/115c20fad199fe9d.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@22", "density": 0.8367105270898347, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "friedman_metric_expression": "2.56740+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5674, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.56740+", "metric_symbol": "s", "metric_value": 2.5674, "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "b3ecf4aa9beda411", "improvement": -0.0050654803778220625, "max_boundary_excess": -3.63122781255133e-06, "max_pair_overlap_depth": -1.9313990747837906e-06, "metric_expression": "2.57247", "metric_symbol": "s", "metric_value": 2.572465480377822, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.5674, "setup": "triinpen", "side": 2.572465480377822, "solution_path": "data/solutions/generated/triinpen_022_b3ecf4aa9beda411.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b3ecf4aa9beda411.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@23", "density": 0.8358219621726138, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "friedman_metric_expression": "2.61831+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61831, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.61831+", "metric_symbol": "s", "metric_value": 2.61831, "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "b2f9cfacd50b72e9", "improvement": -0.013368670719241305, "max_boundary_excess": -5.909725797067009e-06, "max_pair_overlap_depth": -5.3149326107448935e-06, "metric_expression": "2.63168", "metric_symbol": "s", "metric_value": 2.6316786707192414, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.61831, "setup": "triinpen", "side": 2.6316786707192414, "solution_path": "data/solutions/generated/triinpen_023_b2f9cfacd50b72e9.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b2f9cfacd50b72e9.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@24", "density": 0.8203286521496933, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "friedman_metric_expression": "2.66641+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.66641, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.66641+", "metric_symbol": "s", "metric_value": 2.66641, "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "76211a17aba30b36", "improvement": -0.04713802590265814, "max_boundary_excess": -7.766120852076588e-07, "max_pair_overlap_depth": -5.665654174702439e-07, "metric_expression": "2.71355", "metric_symbol": "s", "metric_value": 2.713548025902658, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.66641, "setup": "triinpen", "side": 2.713548025902658, "solution_path": "data/solutions/generated/triinpen_024_76211a17aba30b36.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/76211a17aba30b36.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@25", "density": 0.8170666213083482, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "friedman_metric_expression": "2.720+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.72, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.720+", "metric_symbol": "s", "metric_value": 2.72, "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "cc904cb82492c4b0", "improvement": -0.055026288404456114, "max_boundary_excess": -3.831253149892822e-06, "max_pair_overlap_depth": -1.0171981972284527e-05, "metric_expression": "2.77503", "metric_symbol": "s", "metric_value": 2.7750262884044563, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.72, "setup": "triinpen", "side": 2.7750262884044563, "solution_path": "data/solutions/generated/triinpen_025_cc904cb82492c4b0.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cc904cb82492c4b0.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@26", "density": 0.8287869991439658, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "friedman_metric_expression": "2.771+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.771, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.771+", "metric_symbol": "s", "metric_value": 2.771, "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "810173856676a6fb", "improvement": -0.03890114272185885, "max_boundary_excess": -2.899135639086088e-06, "max_pair_overlap_depth": -1.3139310877985366e-05, "metric_expression": "2.80990", "metric_symbol": "s", "metric_value": 2.8099011427218588, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.771, "setup": "triinpen", "side": 2.8099011427218588, "solution_path": "data/solutions/generated/triinpen_026_810173856676a6fb.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/810173856676a6fb.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@27", "density": 0.8321868307827671, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "friedman_metric_expression": "2.81761+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.81761, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.81761+", "metric_symbol": "s", "metric_value": 2.81761, "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "8b8ba91284e47068", "improvement": -0.03996274171783831, "max_boundary_excess": -3.050950539540987e-07, "max_pair_overlap_depth": -5.479231620197922e-06, "metric_expression": "2.85757", "metric_symbol": "s", "metric_value": 2.8575727417178385, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.81761, "setup": "triinpen", "side": 2.8575727417178385, "solution_path": "data/solutions/generated/triinpen_027_8b8ba91284e47068.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8b8ba91284e47068.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@28", "density": 0.8534363238461394, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "friedman_metric_expression": "2.868+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.868, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.868+", "metric_symbol": "s", "metric_value": 2.868, "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6ad421ad9865e8bf", "improvement": -0.005553490865734201, "max_boundary_excess": -2.0498365378060392e-06, "max_pair_overlap_depth": -1.2746651528505737e-05, "metric_expression": "2.87355", "metric_symbol": "s", "metric_value": 2.873553490865734, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.868, "setup": "triinpen", "side": 2.873553490865734, "solution_path": "data/solutions/generated/triinpen_028_6ad421ad9865e8bf.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6ad421ad9865e8bf.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@29", "density": 0.8464177208582354, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "friedman_metric_expression": "2.903+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.903, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.903+", "metric_symbol": "s", "metric_value": 2.903, "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "0d9d40fe56c0f6d4", "improvement": -0.03351657923241014, "max_boundary_excess": -2.7025059194940577e-06, "max_pair_overlap_depth": -2.3448291092131868e-06, "metric_expression": "2.93652", "metric_symbol": "s", "metric_value": 2.93651657923241, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.903, "setup": "triinpen", "side": 2.93651657923241, "solution_path": "data/solutions/generated/triinpen_029_0d9d40fe56c0f6d4.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0d9d40fe56c0f6d4.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@30", "density": 0.8397676649377761, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "friedman_metric_expression": "2.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.952, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.952+", "metric_symbol": "s", "metric_value": 2.952, "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2b832e7a9fa0a7c5", "improvement": -0.04651955266880892, "max_boundary_excess": -7.656844312442343e-06, "max_pair_overlap_depth": -3.4133589315032964e-06, "metric_expression": "2.99852", "metric_symbol": "s", "metric_value": 2.998519552668809, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.952, "setup": "triinpen", "side": 2.998519552668809, "solution_path": "data/solutions/generated/triinpen_030_2b832e7a9fa0a7c5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2b832e7a9fa0a7c5.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@31", "density": 0.8566123952654375, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "friedman_metric_expression": "2.992+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.992, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.992+", "metric_symbol": "s", "metric_value": 2.992, "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "579de3c893a5a64c", "improvement": -0.025967103693977922, "max_boundary_excess": -1.099100289551188e-06, "max_pair_overlap_depth": -2.29204214511336e-05, "metric_expression": "3.01797", "metric_symbol": "s", "metric_value": 3.017967103693978, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.992, "setup": "triinpen", "side": 3.017967103693978, "solution_path": "data/solutions/generated/triinpen_031_579de3c893a5a64c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/579de3c893a5a64c.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@32", "density": 0.8514556204542924, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "friedman_metric_expression": "3.029+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.029, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.029+", "metric_symbol": "s", "metric_value": 3.029, "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "70ed9a5e30a88f24", "improvement": -0.04652890272981658, "max_boundary_excess": -2.6611165642007356e-06, "max_pair_overlap_depth": -3.1395889643626163e-06, "metric_expression": "3.07553", "metric_symbol": "s", "metric_value": 3.0755289027298165, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.029, "setup": "triinpen", "side": 3.0755289027298165, "solution_path": "data/solutions/generated/triinpen_032_70ed9a5e30a88f24.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/70ed9a5e30a88f24.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@33", "density": 0.872718269558225, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "friedman_metric_expression": "3.078+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.078, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.078+", "metric_symbol": "s", "metric_value": 3.078, "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "13357e078d1002ad", "improvement": -0.006933225403836563, "max_boundary_excess": -1.6488057343371516e-06, "max_pair_overlap_depth": -2.3777449531969808e-05, "metric_expression": "3.08493", "metric_symbol": "s", "metric_value": 3.0849332254038364, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.078, "setup": "triinpen", "side": 3.0849332254038364, "solution_path": "data/solutions/generated/triinpen_033_13357e078d1002ad.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/13357e078d1002ad.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@34", "density": 0.8697735245280512, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "friedman_metric_expression": "3.114+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.114, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.114+", "metric_symbol": "s", "metric_value": 3.114, "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "9cac5218ebb67cb5", "improvement": -0.022622102843430802, "max_boundary_excess": -7.423271733968168e-08, "max_pair_overlap_depth": -2.357396563512637e-06, "metric_expression": "3.13662", "metric_symbol": "s", "metric_value": 3.1366221028434307, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.114, "setup": "triinpen", "side": 3.1366221028434307, "solution_path": "data/solutions/generated/triinpen_034_9cac5218ebb67cb5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9cac5218ebb67cb5.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@35", "density": 0.8649966542185312, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "friedman_metric_expression": "3.150+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.15, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.150+", "metric_symbol": "s", "metric_value": 3.15, "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "e568d5830b049327", "improvement": -0.0411898371667867, "max_boundary_excess": -1.753518123765835e-06, "max_pair_overlap_depth": -1.5568053413739236e-05, "metric_expression": "3.19119", "metric_symbol": "s", "metric_value": 3.1911898371667866, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.15, "setup": "triinpen", "side": 3.1911898371667866, "solution_path": "data/solutions/generated/triinpen_035_e568d5830b049327.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e568d5830b049327.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@36", "density": 0.8954701086953395, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "friedman_metric_expression": "3.177+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.177, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.177+", "metric_symbol": "s", "metric_value": 3.177, "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "94f98697d38e8534", "improvement": -0.003911128614793036, "max_boundary_excess": -2.377739372786898e-06, "max_pair_overlap_depth": -3.2778702236946344e-06, "metric_expression": "3.18091", "metric_symbol": "s", "metric_value": 3.180911128614793, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.177, "setup": "triinpen", "side": 3.180911128614793, "solution_path": "data/solutions/generated/triinpen_036_94f98697d38e8534.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/94f98697d38e8534.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@37", "density": 0.9007684327912503, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.217+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.217, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.217+", "metric_symbol": "s", "metric_value": 3.217, "reference_text": "s = 3.217+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.217+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "id": "f44599d4a9e5e733", "improvement": 0.0017102585047612529, "max_boundary_excess": -3.6104708733830643e-07, "max_pair_overlap_depth": -4.178008898181318e-06, "n": 37, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 3.217, "setup": "triinpen", "side": 3.215289741495239, "solution_path": "data/solutions/triinpen_37.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/f44599d4a9e5e733.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@38", "density": 0.9005911187149712, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.261+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.261, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.261+", "metric_symbol": "s", "metric_value": 3.261, "reference_text": "s = 3.261+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.261+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "id": "05bcab1d7902fa55", "improvement": 0.0022293194217613, "max_boundary_excess": -4.649651923094469e-07, "max_pair_overlap_depth": -2.076724902710936e-06, "n": 38, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 3.261, "setup": "triinpen", "side": 3.258770680578239, "solution_path": "data/solutions/triinpen_38.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/05bcab1d7902fa55.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinpen@39", "density": 0.9025101556269666, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "friedman_metric_expression": "3.295+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.295, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.295+", "metric_symbol": "s", "metric_value": 3.295, "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "67a6bbf24108966a", "improvement": -0.002859023967915597, "max_boundary_excess": -1.9740347935670834e-06, "max_pair_overlap_depth": -1.0007850107629501e-05, "metric_expression": "3.29786", "metric_symbol": "s", "metric_value": 3.2978590239679155, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.295, "setup": "triinpen", "side": 3.2978590239679155, "solution_path": "data/solutions/generated/triinpen_039_67a6bbf24108966a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/67a6bbf24108966a.svg", "tolerance": 1e-08, "verified": true} {"case": "triinpen@40", "density": 0.9090379593265822, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.337+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.337, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.337+", "metric_symbol": "s", "metric_value": 3.337, "reference_text": "s = 3.337+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.337+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "id": "d177c371d1e3f387", "improvement": 0.009141758371615794, "max_boundary_excess": -2.9487074289032124e-07, "max_pair_overlap_depth": -6.944746260284518e-07, "n": 40, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 3.337, "setup": "triinpen", "side": 3.3278582416283844, "solution_path": "data/solutions/triinpen_40.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/d177c371d1e3f387.svg", "tolerance": 1e-08, "verified": true} {"case": "triinsqu@1", "density": 0.4640965865243202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(\u221a2+\u221a6)/4 = .965+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.965, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "(\u221a2+\u221a6)/4 = .965+", "metric_symbol": "s", "metric_value": 0.965, "reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "source_image": "t1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "friedman_source_image": "t1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d0da9c9aae58c37e", "improvement": -0.0009310593101359288, "max_boundary_excess": -7.031269735994051e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.96593", "metric_symbol": "s", "metric_value": 0.9659310593101359, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.965, "setup": "triinsqu", "side": 0.9659310593101359, "solution_path": "data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d0da9c9aae58c37e.svg", "tolerance": 1e-08, "verified": true} {"case": "triinsqu@2", "density": 0.5773345801938596, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a6/2 = 1.224+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.224, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "\u221a6/2 = 1.224+", "metric_symbol": "s", "metric_value": 1.224, "reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "source_image": "t2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "friedman_source_image": "t2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "536a8bec14614050", "improvement": -0.0007615124236886039, "max_boundary_excess": -3.5296142902332335e-06, "max_pair_overlap_depth": -8.602274652714007e-06, "metric_expression": "1.22476", "metric_symbol": "s", "metric_value": 1.2247615124236886, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.224, "setup": "triinsqu", "side": 1.2247615124236886, "solution_path": "data/solutions/generated/triinsqu_002_536a8bec14614050.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/536a8bec14614050.svg", "tolerance": 1e-08, "verified": true} @@ -566,7 +784,26 @@ {"case": "triinsqu@18", "density": 0.8124930238229202, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.051+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.051, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@18", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "4/29/26", "metric_expression": "3.051+", "metric_symbol": "s", "metric_value": 3.051, "reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "e37e7e8bffa4ff54", "improvement": -0.04625348434953214, "max_boundary_excess": -2.7140695543143397e-06, "max_pair_overlap_depth": -2.8845175708891446e-05, "metric_expression": "3.09725", "metric_symbol": "s", "metric_value": 3.0972534843495323, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.051, "setup": "triinsqu", "side": 3.0972534843495323, "solution_path": "data/solutions/generated/triinsqu_018_e37e7e8bffa4ff54.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e37e7e8bffa4ff54.svg", "tolerance": 1e-08, "verified": true} {"case": "triinsqu@19", "density": 0.8324573792569255, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.12930+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1293, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.12930+", "metric_symbol": "s", "metric_value": 3.1293, "reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "source_image": "t19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "b548b946ae0b4ba7", "improvement": -0.01443633599486338, "max_boundary_excess": -4.91075951885532e-06, "max_pair_overlap_depth": -2.901764488139058e-06, "metric_expression": "3.14374", "metric_symbol": "s", "metric_value": 3.1437363359948636, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.1293, "setup": "triinsqu", "side": 3.1437363359948636, "solution_path": "data/solutions/generated/triinsqu_019_b548b946ae0b4ba7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b548b946ae0b4ba7.svg", "tolerance": 1e-08, "verified": true} {"case": "triinsqu@20", "density": 0.8188093166106081, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.2305+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.2305, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.2305+", "metric_symbol": "s", "metric_value": 3.2305, "reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "source_image": "t20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "3081d28a13591fef", "improvement": -0.02167515790076191, "max_boundary_excess": -4.133822536981461e-06, "max_pair_overlap_depth": -2.11952039982366e-05, "metric_expression": "3.25218", "metric_symbol": "s", "metric_value": 3.252175157900762, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.2305, "setup": "triinsqu", "side": 3.252175157900762, "solution_path": "data/solutions/generated/triinsqu_020_3081d28a13591fef.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3081d28a13591fef.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@21", "density": 0.8197746048663628, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "friedman_metric_expression": "3.3111+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3111, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.3111+", "metric_symbol": "s", "metric_value": 3.3111, "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "source_image": "t21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "3debb201d272befe", "improvement": -0.01942528494838358, "max_boundary_excess": -3.1059976134608187e-06, "max_pair_overlap_depth": -1.7605367639283998e-06, "metric_expression": "3.33053", "metric_symbol": "s", "metric_value": 3.3305252849483837, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.3111, "setup": "triinsqu", "side": 3.3305252849483837, "solution_path": "data/solutions/generated/triinsqu_021_3debb201d272befe.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3debb201d272befe.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@22", "density": 0.8320198700821632, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "friedman_metric_expression": "3.3757+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3757, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.3757+", "metric_symbol": "s", "metric_value": 3.3757, "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "source_image": "t22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "470a866027c799dc", "improvement": -0.008023046534652689, "max_boundary_excess": -1.549110939521453e-06, "max_pair_overlap_depth": -9.024431791848642e-07, "metric_expression": "3.38372", "metric_symbol": "s", "metric_value": 3.383723046534653, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.3757, "setup": "triinsqu", "side": 3.383723046534653, "solution_path": "data/solutions/generated/triinsqu_022_470a866027c799dc.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/470a866027c799dc.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@23", "density": 0.825135735506605, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "friedman_metric_expression": "3.4311+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4311, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.4311+", "metric_symbol": "s", "metric_value": 3.4311, "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "source_image": "t23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "23d97af9efc6a19d", "improvement": -0.04307377695172354, "max_boundary_excess": -3.0575531387249386e-07, "max_pair_overlap_depth": -1.3951600157491306e-05, "metric_expression": "3.47417", "metric_symbol": "s", "metric_value": 3.4741737769517234, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.4311, "setup": "triinsqu", "side": 3.4741737769517234, "solution_path": "data/solutions/generated/triinsqu_023_23d97af9efc6a19d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/23d97af9efc6a19d.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@24", "density": 0.857512475445178, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "friedman_metric_expression": "3.468+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.468, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@24", "credit": "Maurizio Morandi", "date": "August 2008", "family_updated": "4/29/26", "metric_expression": "3.468+", "metric_symbol": "s", "metric_value": 3.468, "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "source_image": "t24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "friedman_source_image": "t24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "aa931802df351f6b", "improvement": -0.013254030591762334, "max_boundary_excess": -2.7516785866311762e-06, "max_pair_overlap_depth": -1.795583897323816e-05, "metric_expression": "3.48125", "metric_symbol": "s", "metric_value": 3.4812540305917623, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.468, "setup": "triinsqu", "side": 3.4812540305917623, "solution_path": "data/solutions/generated/triinsqu_024_aa931802df351f6b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/aa931802df351f6b.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@25", "density": 0.8572641065590827, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "friedman_metric_expression": "3.537+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.537, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@25", "credit": "David W", "date": "August 2012", "family_updated": "4/29/26", "metric_expression": "3.537+", "metric_symbol": "s", "metric_value": 3.537, "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "source_image": "t25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "t25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "16117b2f4cd0a5a0", "improvement": -0.016554677577784283, "max_boundary_excess": -2.280886997301251e-06, "max_pair_overlap_depth": -1.0363527685852691e-05, "metric_expression": "3.55355", "metric_symbol": "s", "metric_value": 3.553554677577784, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.537, "setup": "triinsqu", "side": 3.553554677577784, "solution_path": "data/solutions/generated/triinsqu_025_16117b2f4cd0a5a0.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/16117b2f4cd0a5a0.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@26", "density": 0.8564901139309976, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "friedman_metric_expression": "3.575+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.575, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@26", "credit": "Maurizio Morandi", "date": "September 2008", "family_updated": "4/29/26", "metric_expression": "3.575+", "metric_symbol": "s", "metric_value": 3.575, "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "source_image": "t26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "friedman_source_image": "t26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ebfed25c219baa0e", "improvement": -0.050565994245078016, "max_boundary_excess": -2.7124557589233795e-06, "max_pair_overlap_depth": -1.7247237756201628e-05, "metric_expression": "3.62557", "metric_symbol": "s", "metric_value": 3.625565994245078, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.575, "setup": "triinsqu", "side": 3.625565994245078, "solution_path": "data/solutions/generated/triinsqu_026_ebfed25c219baa0e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ebfed25c219baa0e.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@27", "density": 0.8498602034176942, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "friedman_metric_expression": "3.6726+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.6726, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.6726+", "metric_symbol": "s", "metric_value": 3.6726, "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "source_image": "t27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "dbdb303c3aa850bb", "improvement": -0.03641383792443431, "max_boundary_excess": -5.085430993154038e-06, "max_pair_overlap_depth": -1.0288234183475353e-06, "metric_expression": "3.70901", "metric_symbol": "s", "metric_value": 3.7090138379244344, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.6726, "setup": "triinsqu", "side": 3.7090138379244344, "solution_path": "data/solutions/generated/triinsqu_027_dbdb303c3aa850bb.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dbdb303c3aa850bb.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@28", "density": 0.8409752820125738, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "friedman_metric_expression": "3.7571+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7571, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.7571+", "metric_symbol": "s", "metric_value": 3.7571, "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "source_image": "t28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d660009be45656fb", "improvement": -0.03987482885375426, "max_boundary_excess": -4.926402812612589e-06, "max_pair_overlap_depth": -7.738785352429112e-06, "metric_expression": "3.79697", "metric_symbol": "s", "metric_value": 3.796974828853754, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.7571, "setup": "triinsqu", "side": 3.796974828853754, "solution_path": "data/solutions/generated/triinsqu_028_d660009be45656fb.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d660009be45656fb.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@29", "density": 0.8511488797755807, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "friedman_metric_expression": "3.818+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.818, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.818+", "metric_symbol": "s", "metric_value": 3.818, "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "t29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "t29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "580739cf26075b25", "improvement": -0.023019845203774647, "max_boundary_excess": -5.02170884848626e-08, "max_pair_overlap_depth": -7.455986605509057e-06, "metric_expression": "3.84102", "metric_symbol": "s", "metric_value": 3.8410198452037747, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.818, "setup": "triinsqu", "side": 3.8410198452037747, "solution_path": "data/solutions/generated/triinsqu_029_580739cf26075b25.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/580739cf26075b25.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@30", "density": 0.8453943070349464, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "friedman_metric_expression": "3.8662+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.8662, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.8662+", "metric_symbol": "s", "metric_value": 3.8662, "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "source_image": "t30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "c1d8c0f9af9cd320", "improvement": -0.05375684533529945, "max_boundary_excess": -9.869941090398363e-07, "max_pair_overlap_depth": -3.480593055327219e-06, "metric_expression": "3.91996", "metric_symbol": "s", "metric_value": 3.9199568453352995, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.8662, "setup": "triinsqu", "side": 3.9199568453352995, "solution_path": "data/solutions/generated/triinsqu_030_c1d8c0f9af9cd320.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c1d8c0f9af9cd320.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@31", "density": 0.8400189843781062, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "friedman_metric_expression": "3.936+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.936, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.936+", "metric_symbol": "s", "metric_value": 3.936, "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "source_image": "t31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "272c8c45b9a6dd78", "improvement": -0.06148289712739752, "max_boundary_excess": -1.9869012023909734e-06, "max_pair_overlap_depth": -1.1060967226250717e-05, "metric_expression": "3.99748", "metric_symbol": "s", "metric_value": 3.9974828971273975, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.936, "setup": "triinsqu", "side": 3.9974828971273975, "solution_path": "data/solutions/generated/triinsqu_031_272c8c45b9a6dd78.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/272c8c45b9a6dd78.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@32", "density": 0.833007660060693, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "friedman_metric_expression": "3.997+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.997, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.997+", "metric_symbol": "s", "metric_value": 3.997, "reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 2026.", "source_image": "t32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "aa2ff1aceeba9dbd", "improvement": -0.0815032212073783, "max_boundary_excess": -5.66081673195531e-06, "max_pair_overlap_depth": -4.793291196181215e-06, "metric_expression": "4.07850", "metric_symbol": "s", "metric_value": 4.078503221207378, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.997, "setup": "triinsqu", "side": 4.078503221207378, "solution_path": "data/solutions/generated/triinsqu_032_aa2ff1aceeba9dbd.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/aa2ff1aceeba9dbd.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@33", "density": 0.8366415016689572, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "friedman_metric_expression": "4.058+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.058, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.058+", "metric_symbol": "s", "metric_value": 4.058, "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "source_image": "t33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "652d6c2cf21c385c", "improvement": -0.07473526355298876, "max_boundary_excess": -6.365030008288742e-08, "max_pair_overlap_depth": -1.4601549878645592e-06, "metric_expression": "4.13274", "metric_symbol": "s", "metric_value": 4.132735263552989, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.058, "setup": "triinsqu", "side": 4.132735263552989, "solution_path": "data/solutions/generated/triinsqu_033_652d6c2cf21c385c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/652d6c2cf21c385c.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@34", "density": 0.8455895674978956, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "friedman_metric_expression": "4.098+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.098, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.098+", "metric_symbol": "s", "metric_value": 4.098, "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "source_image": "t34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "5f00ff525459125e", "improvement": -0.07463088632816373, "max_boundary_excess": -2.422656501976907e-07, "max_pair_overlap_depth": -3.1602008447872976e-06, "metric_expression": "4.17263", "metric_symbol": "s", "metric_value": 4.172630886328164, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.098, "setup": "triinsqu", "side": 4.172630886328164, "solution_path": "data/solutions/generated/triinsqu_034_5f00ff525459125e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5f00ff525459125e.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@35", "density": 0.8584202751980219, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "friedman_metric_expression": "9(2\u221a3\u20133) = 4.176+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.176, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@35", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "9(2\u221a3\u20133) = 4.176+", "metric_symbol": "s", "metric_value": 4.176, "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "source_image": "t35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "t35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "0fd80a947c5904bb", "improvement": -0.025790132248165953, "max_boundary_excess": -2.0186743648470723e-06, "max_pair_overlap_depth": -1.0972661374369919e-05, "metric_expression": "4.20179", "metric_symbol": "s", "metric_value": 4.201790132248166, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.176, "setup": "triinsqu", "side": 4.201790132248166, "solution_path": "data/solutions/generated/triinsqu_035_0fd80a947c5904bb.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0fd80a947c5904bb.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@36", "density": 0.8656950017914491, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "friedman_metric_expression": "4.214+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.214, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.214+", "metric_symbol": "s", "metric_value": 4.214, "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "source_image": "t36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "73acd05c27fe131e", "improvement": -0.029450235060704877, "max_boundary_excess": -1.6988749159352698e-06, "max_pair_overlap_depth": -1.0359883173549633e-08, "metric_expression": "4.24345", "metric_symbol": "s", "metric_value": 4.243450235060705, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.214, "setup": "triinsqu", "side": 4.243450235060705, "solution_path": "data/solutions/generated/triinsqu_036_73acd05c27fe131e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/73acd05c27fe131e.svg", "tolerance": 1e-08, "verified": true} {"case": "triinsqu@37", "density": 0.8777550041407036, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.276+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.276, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.276+", "metric_symbol": "s", "metric_value": 4.276, "reference_text": "37. | | s = 4.276+ | Found by Emerson Connelly | in April 2026.", "source_image": "t37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "37. | | s = 4.276+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "id": "8735d9f36ada5e93", "improvement": 0.0036726339396722096, "max_boundary_excess": -2.0547460484616992e-07, "max_pair_overlap_depth": -1.528656046745347e-06, "n": 37, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 4.276, "setup": "triinsqu", "side": 4.272327366060328, "solution_path": "data/solutions/triinsqu_37.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/8735d9f36ada5e93.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@38", "density": 0.8696240777565032, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "friedman_metric_expression": "4.327+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.327, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.327+", "metric_symbol": "s", "metric_value": 4.327, "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "source_image": "t38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "a013f42c7873094a", "improvement": -0.0228706067926554, "max_boundary_excess": -2.365499665465618e-06, "max_pair_overlap_depth": -2.5247442803078e-06, "metric_expression": "4.34987", "metric_symbol": "s", "metric_value": 4.349870606792655, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.327, "setup": "triinsqu", "side": 4.349870606792655, "solution_path": "data/solutions/generated/triinsqu_038_a013f42c7873094a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a013f42c7873094a.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@39", "density": 0.8718778943291693, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "friedman_metric_expression": "4.383+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.383, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.383+", "metric_symbol": "s", "metric_value": 4.383, "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "source_image": "t39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "5f6780607ec0989b", "improvement": -0.01803465361730261, "max_boundary_excess": -1.974803491340428e-06, "max_pair_overlap_depth": -1.9608803808246478e-05, "metric_expression": "4.40103", "metric_symbol": "s", "metric_value": 4.401034653617303, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.383, "setup": "triinsqu", "side": 4.401034653617303, "solution_path": "data/solutions/generated/triinsqu_039_5f6780607ec0989b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5f6780607ec0989b.svg", "tolerance": 1e-08, "verified": true} +{"case": "triinsqu@40", "density": 0.878868813713771, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "friedman_metric_expression": "4.437+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.437, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.437+", "metric_symbol": "s", "metric_value": 4.437, "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "source_image": "t40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ccf2360cc8917adc", "improvement": -0.002338759632142029, "max_boundary_excess": -2.520888573265893e-06, "max_pair_overlap_depth": -1.6780429565876886e-05, "metric_expression": "4.43934", "metric_symbol": "s", "metric_value": 4.439338759632142, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.437, "setup": "triinsqu", "side": 4.439338759632142, "solution_path": "data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ccf2360cc8917adc.svg", "tolerance": 1e-08, "verified": true} {"case": "triintri@1", "density": 0.9999824309457177, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@1", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "tt1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "tt1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "cc844f952409d64a", "improvement": -8.784642894887895e-06, "max_boundary_excess": -1.727739205730037e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000087846428949, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "triintri", "side": 1.0000087846428949, "solution_path": "data/solutions/generated/triintri_001_cc844f952409d64a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cc844f952409d64a.svg", "tolerance": 1e-08, "verified": true} {"case": "triintri@2", "density": 0.49997366021738365, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@2", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "666ea688ab3bec3c", "improvement": -5.2681646676600025e-05, "max_boundary_excess": -9.520753462741007e-07, "max_pair_overlap_depth": -2.9199608040486602e-05, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.0000526816466766, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0000526816466766, "solution_path": "data/solutions/generated/triintri_002_666ea688ab3bec3c.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/666ea688ab3bec3c.svg", "tolerance": 1e-08, "verified": true} {"case": "triintri@3", "density": 0.7499622672788224, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@3", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "92df600f3a6e54a1", "improvement": -5.031219332751746e-05, "max_boundary_excess": -1.3199738659319715e-06, "max_pair_overlap_depth": -1.9954872927441247e-05, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.0000503121933275, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0000503121933275, "solution_path": "data/solutions/generated/triintri_003_92df600f3a6e54a1.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92df600f3a6e54a1.svg", "tolerance": 1e-08, "verified": true} @@ -587,4 +824,23 @@ {"case": "triintri@18", "density": 0.8888203671574908, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "9/2 = 4.500", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "2/29/26", "metric_expression": "9/2 = 4.500", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "source_image": "tt18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b4cfb14015aca75a", "improvement": -0.00017345566104154386, "max_boundary_excess": -2.575746594607548e-06, "max_pair_overlap_depth": -5.0550449839370515e-06, "metric_expression": "4.50017", "metric_symbol": "s", "metric_value": 4.5001734556610415, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.5, "setup": "triintri", "side": 4.5001734556610415, "solution_path": "data/solutions/generated/triintri_018_b4cfb14015aca75a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4cfb14015aca75a.svg", "tolerance": 1e-08, "verified": true} {"case": "triintri@19", "density": 0.872322152073677, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "14/3 = 4.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.666, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@19", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "14/3 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "bf4e89c9b4dd8ae2", "improvement": -0.0010058992763006813, "max_boundary_excess": -5.331642222161759e-07, "max_pair_overlap_depth": -9.690072424628493e-06, "metric_expression": "4.66701", "metric_symbol": "s", "metric_value": 4.667005899276301, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.666, "setup": "triintri", "side": 4.667005899276301, "solution_path": "data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bf4e89c9b4dd8ae2.svg", "tolerance": 1e-08, "verified": true} {"case": "triintri@20", "density": 0.838067095701634, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.861, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@20", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "metric_symbol": "s", "metric_value": 4.861, "reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "53a8c84cf6eae28f", "improvement": -0.02412412405335207, "max_boundary_excess": -1.1914189120695684e-06, "max_pair_overlap_depth": -6.957564219201018e-07, "metric_expression": "4.88512", "metric_symbol": "s", "metric_value": 4.885124124053352, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.861, "setup": "triintri", "side": 4.885124124053352, "solution_path": "data/solutions/generated/triintri_020_53a8c84cf6eae28f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/53a8c84cf6eae28f.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@21", "density": 0.8399445306050737, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "friedman_metric_expression": "4.923+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.923, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "4.923+", "metric_symbol": "s", "metric_value": 4.923, "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "51d32dd1bf4348fb", "improvement": -0.0771650956615133, "max_boundary_excess": -2.830489805416455e-06, "max_pair_overlap_depth": -5.709825519950584e-06, "metric_expression": "5.00017", "metric_symbol": "s", "metric_value": 5.000165095661513, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.923, "setup": "triintri", "side": 5.000165095661513, "solution_path": "data/solutions/generated/triintri_021_51d32dd1bf4348fb.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/51d32dd1bf4348fb.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@22", "density": 0.8799245341930954, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "friedman_metric_expression": "4.996+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.996, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@22", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "4.996+", "metric_symbol": "s", "metric_value": 4.996, "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2122d833c6fcab70", "improvement": -0.004214405286988132, "max_boundary_excess": -5.380108740330726e-08, "max_pair_overlap_depth": -8.335028905959163e-07, "metric_expression": "5.00021", "metric_symbol": "s", "metric_value": 5.000214405286989, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.996, "setup": "triintri", "side": 5.000214405286989, "solution_path": "data/solutions/generated/triintri_022_2122d833c6fcab70.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2122d833c6fcab70.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@23", "density": 0.9199301650083309, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@23", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "c27df81200778ffb", "improvement": -0.00018977980346601697, "max_boundary_excess": -6.179779071167411e-07, "max_pair_overlap_depth": -4.1714675197424e-07, "metric_expression": "5.00019", "metric_symbol": "s", "metric_value": 5.000189779803466, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.000189779803466, "solution_path": "data/solutions/generated/triintri_023_c27df81200778ffb.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c27df81200778ffb.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@24", "density": 0.9599250294051547, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@24", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "c9e2b321b60a0e78", "improvement": -0.00019524735994114195, "max_boundary_excess": -2.7221451237306384e-06, "max_pair_overlap_depth": -1.3704928858437881e-07, "metric_expression": "5.00020", "metric_symbol": "s", "metric_value": 5.000195247359941, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.000195247359941, "solution_path": "data/solutions/generated/triintri_024_c9e2b321b60a0e78.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c9e2b321b60a0e78.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@25", "density": 0.9999421250190796, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@25", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5092959dfa8a0e27", "improvement": -0.0001446937329419029, "max_boundary_excess": -1.7535771332062027e-06, "max_pair_overlap_depth": -7.792197432854309e-07, "metric_expression": "5.00014", "metric_symbol": "s", "metric_value": 5.000144693732942, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.000144693732942, "solution_path": "data/solutions/generated/triintri_025_5092959dfa8a0e27.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5092959dfa8a0e27.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@26", "density": 0.8757579251966457, "friedman_analytical_or_proved": false, "friedman_credit": "Joah Frenzley", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "friedman_metric_expression": "5.406+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.406, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@26", "credit": "Joah Frenzley", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "5.406+", "metric_symbol": "s", "metric_value": 5.406, "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "source_image": "tt26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "friedman_source_image": "tt26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8db318b73d49217d", "improvement": -0.04272181972430644, "max_boundary_excess": -1.2897298944239458e-06, "max_pair_overlap_depth": -1.0218222609881256e-05, "metric_expression": "5.44872", "metric_symbol": "s", "metric_value": 5.448721819724306, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.406, "setup": "triintri", "side": 5.448721819724306, "solution_path": "data/solutions/generated/triintri_026_8db318b73d49217d.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8db318b73d49217d.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@27", "density": 0.8924996192164427, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "2/29/26", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "f1c2be61e829f1e2", "improvement": -0.00019215549305418023, "max_boundary_excess": -1.8365186496628e-06, "max_pair_overlap_depth": -1.8064988390742442e-06, "metric_expression": "5.50019", "metric_symbol": "s", "metric_value": 5.500192155493054, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500192155493054, "solution_path": "data/solutions/generated/triintri_027_f1c2be61e829f1e2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f1c2be61e829f1e2.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@28", "density": 0.9255631973649003, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "2/29/26", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "9562d7d6e075a347", "improvement": -0.00016827626559567932, "max_boundary_excess": -2.296352348617567e-06, "max_pair_overlap_depth": -7.147352432124165e-08, "metric_expression": "5.50017", "metric_symbol": "s", "metric_value": 5.500168276265596, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500168276265596, "solution_path": "data/solutions/generated/triintri_028_9562d7d6e075a347.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9562d7d6e075a347.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@29", "density": 0.823477123057378, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "July 2007", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "friedman_metric_expression": "17/3 = 5.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.666, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@29", "credit": "David W", "date": "July 2007", "family_updated": "2/29/26", "metric_expression": "17/3 = 5.666+", "metric_symbol": "s", "metric_value": 5.666, "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "source_image": "tt29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "friedman_source_image": "tt29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "1e26d810ba567eb4", "improvement": -0.2683509950166121, "max_boundary_excess": -5.6694191623693234e-06, "max_pair_overlap_depth": -2.9353541475263256e-07, "metric_expression": "5.93435", "metric_symbol": "s", "metric_value": 5.9343509950166125, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.666, "setup": "triintri", "side": 5.9343509950166125, "solution_path": "data/solutions/generated/triintri_029_1e26d810ba567eb4.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1e26d810ba567eb4.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@30", "density": 0.8727149559817791, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "friedman_metric_expression": "23/4 = 5.75", "friedman_metric_symbol": "s", "friedman_metric_value": 5.75, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@30", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "23/4 = 5.75", "metric_symbol": "s", "metric_value": 5.75, "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "source_image": "tt30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "1ace87e09c5f6fc8", "improvement": -0.11306107243262797, "max_boundary_excess": -1.1340847276256848e-05, "max_pair_overlap_depth": -5.548494655616132e-06, "metric_expression": "5.86306", "metric_symbol": "s", "metric_value": 5.863061072432628, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.75, "setup": "triintri", "side": 5.863061072432628, "solution_path": "data/solutions/generated/triintri_030_1ace87e09c5f6fc8.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1ace87e09c5f6fc8.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@31", "density": 0.8655205028371107, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "friedman_metric_expression": "5.912+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.912, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "5.912+", "metric_symbol": "s", "metric_value": 5.912, "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "source_image": "tt31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "tt31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "e94aa7c2fc600373", "improvement": -0.07269699341354574, "max_boundary_excess": -1.1753168632427688e-06, "max_pair_overlap_depth": -1.577861272879927e-05, "metric_expression": "5.98470", "metric_symbol": "s", "metric_value": 5.984696993413546, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.912, "setup": "triintri", "side": 5.984696993413546, "solution_path": "data/solutions/generated/triintri_031_e94aa7c2fc600373.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e94aa7c2fc600373.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@32", "density": 0.8888356604955802, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "friedman_metric_expression": "5.951+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.951, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@32", "credit": "Ian Watson", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "5.951+", "metric_symbol": "s", "metric_value": 5.951, "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "source_image": "tt32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "ea3eb3c434a6db88", "improvement": -0.049179653895976116, "max_boundary_excess": -2.19130606600491e-06, "max_pair_overlap_depth": -2.006545093746759e-06, "metric_expression": "6.00018", "metric_symbol": "s", "metric_value": 6.000179653895976, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.951, "setup": "triintri", "side": 6.000179653895976, "solution_path": "data/solutions/generated/triintri_032_ea3eb3c434a6db88.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ea3eb3c434a6db88.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@33", "density": 0.9165918569883487, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@33", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5e7c3bf3ddd6ef7e", "improvement": -0.0002448466611522093, "max_boundary_excess": -4.630617313298577e-07, "max_pair_overlap_depth": -7.583551231427066e-09, "metric_expression": "6.00024", "metric_symbol": "s", "metric_value": 6.000244846661152, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000244846661152, "solution_path": "data/solutions/generated/triintri_033_5e7c3bf3ddd6ef7e.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5e7c3bf3ddd6ef7e.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@34", "density": 0.944346274522294, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@34", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "ec0928eb613cde82", "improvement": -0.0003118581825578559, "max_boundary_excess": -1.3696973961467693e-06, "max_pair_overlap_depth": -5.928110144992615e-07, "metric_expression": "6.00031", "metric_symbol": "s", "metric_value": 6.000311858182558, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000311858182558, "solution_path": "data/solutions/generated/triintri_034_ec0928eb613cde82.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ec0928eb613cde82.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@35", "density": 0.9721621988323501, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@35", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "e1b770e700ac967a", "improvement": -0.00018522360819872574, "max_boundary_excess": -2.5752242400016007e-06, "max_pair_overlap_depth": -5.014035051667667e-07, "metric_expression": "6.00019", "metric_symbol": "s", "metric_value": 6.000185223608199, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000185223608199, "solution_path": "data/solutions/generated/triintri_035_e1b770e700ac967a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e1b770e700ac967a.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@36", "density": 0.9999547600515969, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@36", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8e7fac2536d01e26", "improvement": -0.00013572445035237024, "max_boundary_excess": -1.1037978552332137e-06, "max_pair_overlap_depth": -5.02408139535504e-08, "metric_expression": "6.00014", "metric_symbol": "s", "metric_value": 6.000135724450352, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000135724450352, "solution_path": "data/solutions/generated/triintri_036_8e7fac2536d01e26.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8e7fac2536d01e26.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@37", "density": 0.9223731676430976, "friedman_analytical_or_proved": true, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "friedman_metric_expression": "19/3 = 6.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.333, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@37", "credit": "Ian Watson", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "19/3 = 6.333+", "metric_symbol": "s", "metric_value": 6.333, "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "source_image": "tt37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "a824891b660555f5", "improvement": -0.0005547879590457327, "max_boundary_excess": -2.1058084789851627e-06, "max_pair_overlap_depth": -1.0503324543442716e-06, "metric_expression": "6.33355", "metric_symbol": "s", "metric_value": 6.333554787959046, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.333, "setup": "triintri", "side": 6.333554787959046, "solution_path": "data/solutions/generated/triintri_037_a824891b660555f5.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a824891b660555f5.svg", "tolerance": 1e-08, "verified": true} {"case": "triintri@38", "density": 0.917799816589891, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "6.436+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.436, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "6.436+", "metric_symbol": "s", "metric_value": 6.436, "reference_text": "s = 6.436+ | Found by Emerson Connelly | in April 2026.", "source_image": "tt38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6.436+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "tt38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "id": "44f351bb9dc615aa", "improvement": 0.0014554065684695416, "max_boundary_excess": -1.300761040461767e-07, "max_pair_overlap_depth": -1.4944448277348643e-06, "n": 38, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 6.436, "setup": "triintri", "side": 6.43454459343153, "solution_path": "data/solutions/triintri_38.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/44f351bb9dc615aa.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@39", "density": 0.922995893638428, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@39", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5ff069bd30790b7f", "improvement": -0.0002853099319573005, "max_boundary_excess": -2.7141701112233934e-06, "max_pair_overlap_depth": -2.524988351737534e-07, "metric_expression": "6.50029", "metric_symbol": "s", "metric_value": 6.500285309931957, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.500285309931957, "solution_path": "data/solutions/generated/triintri_039_5ff069bd30790b7f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5ff069bd30790b7f.svg", "tolerance": 1e-08, "verified": true} +{"case": "triintri@40", "density": 0.9466291268019702, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@40", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "7890a1da940c9143", "improvement": -0.00039973752172350885, "max_boundary_excess": -3.4343626129297504e-07, "max_pair_overlap_depth": -3.1212060811469655e-06, "metric_expression": "6.50040", "metric_symbol": "s", "metric_value": 6.5003997375217235, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.5003997375217235, "solution_path": "data/solutions/generated/triintri_040_7890a1da940c9143.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7890a1da940c9143.svg", "tolerance": 1e-08, "verified": true}